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/ 

GUY'S 



ELEMENTS OF ASTRONOMY, 



AND 



AN ABRIDGMENT 



OF 



KEITH'S NEW TREATISE 



ON THE 



USE OF THE GLOBES. 



W AMERICAN EDITION, WITH ADDITIONS AND IMPROVEMENTS, AND 
AN EXPLANATION OF THE ASTRONOMICAL PART OF THE 

AMERICAN ALMANAC. 



PHILADELPHIA : 




KEY, MIELKE & BLDDLE, 181 MARKET ST. 

STEREOTYPED BY L. JOHNSON. 

1832. 
1 



2ElXteretr according to the ^ct of (Ecngtcss in the year 1832 
by Key >k> Mielke, in the Clerk's Office of the District Court of 
the Eastern District of Pennsylvania. 



4 



3>L 



PREFACE. 

That Astronomy is now considered a needful and im- 
portant branch of knowledge for every well educated person, 
will be readily allowed; for however some minds, totally 
uncultivated, may, "with brute unconscious gaze," raise 
their eyes to the starry firmament, or behold the various 
phenomena that result therefrom, still, to those who hold a 
respectable rank in society, a general acquaintance at least, 
with the order of the heavenly bodies, and the laws by which 
they are governed, must at some time necessarily become a 
part of their inquiries. 

Hence, where it is practicable, it seems highly desirable 
that that which must be known should be begun early, or 
made a branch of school education ; at least the elements of 
the science, or great leading principles should be then in- 
culcated. 

That there are many great and scientific works, and some 
popular volumes already published, is well known ; and if 
this compendium is added to the number, it is not for the 
sake of obtruding the author once more before that public 
which has so favourably countenanced his former works, but 
because he has not, after a solicitous search, found any trea- 
tise expressly designed and practically drawn up as a class 
book for schools. 

He acknowledges the free use which has been allowed 
him of some works on the subject, from which he has ex- 
tracted valuable materials. Indeed, in a few instances, it 
will be seen that he has preferred rather to select verbatim 
from respectable authorities, than to distort the sentences 
(as is sometimes done) for the sake of an apparent originality. 
Far, however, from attempting to set aside the use of those 
valuable works which should have a place in every library, 
this is intended only to become the handmaid to them. 

3 



IV PREFACE. 

As the study of the same branch of science is often com- 
menced by persons, not only of different ages, but of different 
capacities, and variously circumstanced in point of assistance, 
so must the modes of instruction, and the treatises propor- 
tionably vary. That treatise which may be well adapted to 
the solitary and self-taught student, or that which may, by 
its diversified reflections, captivate a leisure hour, may not 
be the best suited to the boy who studies in conjunction with 
his class fellows, and with the elucidations of a master 
always at hand. 

As an elementary work, care has been taken to avoid two 
very common evils, — that of extreme brevity on the one 
hand, and of a too great prolixity on the other. A mere out- 
line, or brief mention of a very few leading particulars, could 
not prove satisfactory, either to teacher or learner ; it would 
call forth no exertion, excite no interest, afford no pleasure, 
impress no lasting improvement. On the other hand, to 
swell the volume with complicate calculations, and by the 
discussion of subjects too abstruse for juvenile comprehen- 
sion, w ild occasion the Tyro to stumble at the threshold, 
and rec il from the study in hopeless disgust. 

Th' axt or larger print, may be considered to contain the 
general principles and well authenticated facts ; or at least, 
so much of the outline of the science as should be first known. 
This therefore may be appointed for the learner's first course. 

The smaller print, except what refers to illustrations of 
the plates may be omitted, or not formally insisted on, till the 
second course; as it contains matters either less known, or of 
less immediate importance ; or else more difficult to be com- 
prehended. 

Perhaps there is not a point in which instructors more 
widely differ than in their opinion of the quantum proper to 
be put before the pupil. The vast dissimilarity in the bulk 
of elementary treatises, on any one subject, proves the truth 
of this assertion. One teacher prefers a volume for his pupil 



PREFACE. V 

that contains almost every minutia, though it may require 
the toil of years to wade through it ; — another presents him 
with a meagre outline that will not require the labour of as 
many months. 

While this difference of opinion exists, and it will more or 
less ever exist, it may be desirable to meet, as much as pos- 
sible, the views of each. This has been attempted in some 
late publications ; and the plan is here followed by a distinc- 
tion in the type. It is herein intended, that the text, if 
perused alone, should contain in itself a connected and tole- 
rable complete outline ; and if read with the smaller type, 
that the work should exhibit but a more enlarged whole. 
This simplicity in the arrangement will, it is hoped, render 
it more accommodating to instructors, and suit it to the pur- 
poses of scholars of different classes, capacities and ages. 
That work must surely possess some advantages, that can be 
perused by the younger scholar without perplexity, and by 
the more advanced student without deficiency. 

General principles only of an art or science, it is well 
known, are the parts proper to be first committed to nemory ; 
and that too, perhaps, at an age when their utilit is not 
known, nor to what purposes they are applicable, ^his is 
best effected, as Dr. Lowth observes, "by some stfoA and 
clear system." Every one is aware of the impropriety of 
surcharging the bodily organs, — but overloading the yet un- 
expanded faculties of the mind, by an attempt to fill it with 
a too great redundancy of ideas in a first course, is equally 
fruitless and injurious. 

It is particularly recommended that those young persons 
who wish to derive information from this treatise, will not 
only peruse it deliberately, and digest what they read, but 
make a study of it, so as to be able to answer with consider- 
able correctness the questions subjoined. From a mere cur- 
sory perusal, neither information nor entertainment can be 
expected. 

a2 



VI PREFACE. 

It is hoped that the numerous well executed 'plates which 
accompany this work will be deemed appropriate to elucidate 
the subjects ; and that the complete series of questions will 
prove generally acceptable to instructors, and contribute to 
facilitate their labours. 

It is presumed that most of the interesting parts of Astro- 
nomy have been introduced. To have illustrated the method 
of calculating Eclipses, and the transits of Mercury and Ve- 
nus ; or of finding the longitude and the periodic times and 
distances of Jupiter's satellites, &c. might have enhanced 
the work in the public estimation, but to the learner it would 
prove not only useless, but perplexing and obscure. 

Indeed, to have handled the subject more abstrusely, and 
to have written in all the technical phraseology of the science, 
would have been much more easy than was the frequent la- 
bour of verbal discrimination, of casting into shade some 
parts which would only dazzle and bewilder, and of clothing' 
other parts in a language, not less pure it is hoped, but at 
least more suited to the youthful comprehension. 



CONTENTS. 



CHAPTER I. 

Preliminary Definitions 

CHAPTER II. 

Of the Heavenly Bodies 
The Sun 

CHAPTER HI. 

Mercury 

Venus .... 



CHAPTER IV. 
The Earth . 
The Moon 

CHAPTER V. 



Mars 

Asteroids 

CHAPTER VI. 
Jupiter .... 
Jupiter's Satellites 

CHAPTER VII. 

Saturn . 

Satellites of Saturn 
Saturn's Ring 

CHAPTER VIII. 

The Georgium Sidus, or Her 

schel .... 

The Herschel's Satellites 

The Proportional Magnitude 

and Distance of the Planets 

CHAPTER IX. 
Comets 

CHAPTER X. 

The Fixed Stars . 

CHAPTER XI. 

Constellations 
Northern Constellations 
Southern Constellations 
Zodiacal Constellations . 

CHAPTER XII. 
Different Systems . 

CHAPTER Xin. 
Of the Motions of the Planets 



10 
11 



11 
15 

17 

18 



20 
ib. 
21 



22 
23 

ib. 

24 

26 

30 
31 
32 
33 

34 

36 | 



41 
44 



Inferior and Superior Con- 
junctions of the Planets 

CHAPTER XIV. 

The Plane of an Orbit, Pla- 
nets, Node.:, &c. 

The Transiuol" Mercury and 
Venus \ '. 

CHAPTER XV. 

The Ecliptic, Zodiac, and 

Equator, &c. '• . 
Of the Ephemerifc . 

CHAPTER XVI. 

Definitions, Degrees, Poles, &c. 48 

CHAPTER XVII. 
Planets' Orbits Elliptical . 51 
Attraction of Gravitation . ib. 

CHAPTER XVIII. 
Of Attractive and Projectile 
forces 54 

CHAPTER XIX. 
On the Centre of Gravity 
The Horizon . 



CHAPTER XX. 

Day and Night 

CHAPTER XXI. 

Of the Atmosphere 

CHAPTER XXII. 
Refraction . 

CHAPTER XXIII. 
Parallax . 

CHAPTER XXIV 

Equation of Time . 

CHAPTER XXV. 
The Seasons .... 

CHAPTER XXVI. 

The Seasons, continued 

CHAPTER XXVII. 
The Moon's Months, Phases, 
&c 

7 



57 

58 

59 
61 
63 
64 
65 
69 
71 



73 



Vlll 



CONTENTS, 



The Phases of the Moon 74 

CHAPTER XXVIII. 

Eclipses . . 75 

Eclipse of the Moon . . 76 
Eclipse of the Sun . .77 

CHAPTER XXIX. 

Polar Day and Night, &c. . 79 

CHAPTER XXX. 

Umbra and Penumbra in 
Eclipses . . - . .81 

CHAPTER iXXI. 
The Transit of Venus . . 84 
Occultation of the >*xed Stars 86 

CHAPTER XXXII. 

The Harvest Mooa . . 87 

CHAPTER XXXni. 

The Harvest Moon, continued 90 

CHAPTER XXXIV. 
Of Leap-year .... 92 



CHAPTER XXXV. 
The Tides .... 95 

CHAPTER XXXVI. 

The Tides, continued . . 98 

CHAPTER XXXVII. 

The Tides, continued . . 100 

CHAPTER XXXVIII. 

The Precession of the Equinox 104 

CHAPTER XXXIX. 

The Precession of the Equi- 
nox, continued . . . 107 

CHAPTER XL. 

The Obliquity of the Ecliptic, 
&c 



CHAPTER XLI. 

To find the Proportionate 
Magnitudes of the Planets 

To find the Planets Distances 
from the Sun 

Questions for Examination . 



109 

111 

ib. 
113 



EXPLANATION OF SIGNS. 



O The Sun. 
d The Moon. 
® The Earth. 
$ Mercury. 
? Venus. 
t Mars. 



IL Jupiter. 



J? 


Saturn. 


tf 


Uranus. 


? 


Ceres. 


9 


Pallas. 


? 


Juno. 


fi 


Vesta. 



fxifie I 




ELEMENTS OF ASTRONOMY. 



CHAPTER I. 

PRELIMINARY DEFINITIONS. 

Astronomy is that branch of natural philosophy 
which treats of the heavenly bodies : it consists of two 
parts, namely, descriptive and physical Astronomy. 

Descriptive Astronomy, comprises an account of the 
phenomena of the heavenly bodies. 

Physical Astronomy consists in the investigation of 
the causes of their motions, &c. 

A Circle is a plain figure, bounded by a uniform 

curve line, called the circumference, which is every 

where equidistant from a certain point within, called 

its centre, as A B C D (pi. 1. fig. 1.) 

The circumference itself is often called a circle, and also the peri- 
phery. 

The Radius of a circle is a line drawn from the 
centre to the circumference ; as A E, E B, or E C 

(% 1.) 
The Diameter of a circle is a line drawn through the 

centre, and terminated at both ends by the circum- 
ference, as A EC (fig. 1.) 

Every Diameter is double the radius, and divides the circle into two 
equal parts. The terminating points of the diameter are sometimes 
called its Poles, as A and C. 

An Arc of a circle is any part of the circumference, 
asFDG(fig, 1.) 

1 



2 DEFINITIONS. 

A Chord of a circle is a right line joining the ends 
of an arc ; dividing the circle into two unequal parts, 
asFG(fig. I.) 

A Semicircle is half the circle, or a segment cut off 
by the diameter, as A B C (fig. 1.) 

The half circumference is sometimes called the Semicircle. 

A Quadrant is half a semicircle, or one fourth part 
of a whole circle ; as A E B, or B E C. 

A quarter of the circumference is sometimes called a Quadrant. 

All circles, great or small, are supposed to be di- 
vided into 360 equal parts, called degrees (marked ° ;) 
each degree into 60 minutes (marked ' ;) each minute 
into 60 seconds (marked ".) Hence a semicircle con- 
tains 180 degrees, and a quadrant 90 degrees. 

An Angle is the meeting of two lines in a point, as 
A (plate 1, ffg. 2.) 

The point where they meet is called the angular point, and the lines 
A B and A C, are called sides or legs. 

A Right Angle is that which is made by one line 
perpendicular to another, or, when the angles on each 
side are equal to one another, they are right angles ; 
as the angles M and N (fig. 3.) 

The measure of a right angle is a quadrant of 90 degrees. 

An Acute Angle is less than a right angle, as the 
angle S (fig. 4.) 

An Obtuse Angle is greater than a right angle, as 
the angle R (fig. 4.) 

Parallel Lines, whether straight or circular, are 
lines in the same plane, which are every where at the 
same distance from one another; and which, though 
drawn ever so far, both ways, will never meet : thus 



DEFINITIONS. 3 

b and c d and ef (fig. 5,) arc three parallel lines ; 

d g h and i k (fig. 6,) arc two parallel semicircles. 

A Globe or Sphere is a round body, every part of 
vhose surface is equally distant from a point within, 
called its centre. 

A Spheroid is a figure nearly spherical, either ob- 
ong or oblate. The earth is a spheroid, having its axis 
>r diameter at the poles shorter than at the equator. 

A Great Circle, A B D E, of a sphere, is one whose 
plane passes through its centre C. (See plate 2, fig. 1.) 

A Small Circle of a sphere, F G H I, is that whose 
plane does not pass through its centre. 

A Diameter, N C S, of a sphere, perpendicular to 
any great circle, is called the axis of that great circle, 
and the extremities, N S, of the axis, are called its 
poles. (Plate 2, fig. 1.) 

Hence the pole of a great circle is 90° from every point of the di- 
ameter upon the sphere ; because every angle, as NC A, being a right 
angle, the arc, N A, is every where 90 degrees. 

Any two great circles bisect each other ; for the planes of both 
passing through the centre of the sphere, their common section must 
be a diameter of each ; and every diameter bisects a circle. 

The Axis of the earth is that diameter about which 

it performs its diurnal revolution. — See plate 2, fig. 2, 

where p e p a represent the Earth, and p O p the axis. 



CHAPTER II. 

Astronomy is that science which teaches the know- 
ledge of the celestial bodies, the sun, moon, planets, 
comets, and fixed stars ; with their magnitudes, mo- 
tions, distances, periods, eclipses, and order. 



4 DEFINITIONS. 

The general opinion of astronomers of the present day is, that the 
universe is composed of an infinite number of systems of worlds : in 
each of which there are certain bodies moving in free space, and re- 
volving, at different distances, round a sun, placed in or near the centre 
of each system ; and that these suns are the stars which are seen in 
the heavens. 

Among the heavenly bodies the Sun and Moon 
are termed luminaries; the others are called stars. 
Stars are also distinguished into planets and fixed 
stars. 

The Planets, though they appear like the fixed 
stars, are all opaque, or dark bodies, moving in a regu- 
lar order round the sun, from west by south, to east, 
receiving their light from him, and shining by reflecting 
his light. 

Some of the planets have attendants or satellites 
moving round them, as their centres, and with them 
round the sun. There is also another order, called 
comets, with blazing tails, which pursue very eccen- 
tric courses. 

The names of the planets are Mercury, Venus, the 
Earth, Mars, Jupiter, Saturn, and Uranus or Herschel ; 
with four smaller ones, called Asteroids, namely, 
Vesta, Ceres, Pallas, and Juno. 

Vesta, though the last discovered of the asteroids, is, according to 
some authorities, nearer to Mars than either of the other three ; but, 
according to others, Juno is placed the nearest. 

These are all called primaries ; and there are also 
eighteen satellites or moons, called secondaries. The 
Earth has one ; Jupiter, four ; Saturn, seven ; and 
Uranus, six. No moons have hitherto been disco- 
vered to belong to the other planets. 



riot. 





THE SUN. O 

Correctly speaking, the satellites are planets, as well as those round 
which they revolve ; for planet is derived from the Greek word 

7ryxvy,TK, signifying roving or wandering. 

THE SUN. 
The Sun is the source of light and heat, and the 
centre of our Solar or Planetary System. His form is 
nearly that of a sphere or globe. His diameter is 
about 883,210 miles, and his circumference 2,774,692 
miles. 

According to some authorities the Sun's diameter is 893,522 miles. 
For the definition of a globe or sphere, see the Preliminary Definitions, 
Chap. I. The Sun's diameter is equal to 112 diameters of the earth. 

His distance from the earth is 95,000,000 of miles ; 

and he is 1,400,000 times larger than our earth. The 

Sun was for ages, and till lately, thought to be a 'globe 

of real fire ; but it is now supposed to be an opaque 

body, surrounded by a luminous atmosphere. 

Though to the Sun our earth is indebted for light and heat, life and 
vegetation, and without its genial influence it would become a dark 
inert mass, yet Dr. Herschel supposes the Sun to be an opaque body, 
surrounded by a lucid and transparent atmosphere ; that this luminary 
differs but little in his nature from the planets ; and that it is an in- 
habitable world. 

A number of maculae, or dark spots, may sometimes 
be seen, by means of a telescope, on different parts 
of the Sun's surface. These consist of a nucleus, 
which is much darker than the rest, surrounded by a 
mist or smoke ; and they are so changeable as fre- 
quently to vary during the time of observation. Some 
of the largest of them seem to exceed the bulk of the 
whole earth, and are often seen, at intervals of a fort- 
night, for three months together. The darker spots are 
termed maculx, and the brighter faculds. 

B 



b THE SUN. 

The macules have been supposed by some, to be cavities in the body 
of the Sun ; the nucleus being in the bottom of the excavation ; and the 
shady zone surrounding it, the shelving sides of the cavity. Others 
have supposed maculae to be large portions of opaque matter movuig 
in the fiery fluid. Some again have taken them for the smoke of vol- 
canoes in the Sun, or the scum floating upon a huge ocean of fluid 
matter. Faculce, on the contrary, have been called clouds of light, and 
luminous vapours. But Dr. Herschel supposes that the Sun is surround- 
ed by an atmosphere of a phosphoric nature, composed of various trans- 
parent and elastic fluids, by the decomposition of which, light is pro- 
duced, and lucid appearances formed, of different degrees and intensity. 

The Sun has two motions ; the one is a periodical 
motion, in nearly a circular direction round the com- 
mon centre of all the planetary motions (see the arti- 
cle, Centre of Gravity, Chap. XIX.) — the other motion 
is a revolution upon its axis, which is completed in 
about twenty-five days. 

The Sun's motion about its axis renders it spheroidical, having its 
diameter at the equator longer than at the poles. 

The method of ascertaining the Sun's revolution on 
his axis is, by observing the motion of some of those 
remarkable spots which are seen on his disc. If these 
spots are observed uniformly to change their places, 
and to appear on one side and disappear on the other, 
there is not any other means of explaining such phe- 
nomena, but that of a rotation about his axis. 

The time of rotation may be found by observing the 
arc described by any spot in a given time, and then find 
by proportion the time of describing the whole circle. 
Or the return of the spot to the same position with re- 
spect to the earth may be observed, which will give the 
time of an entire rotation. 

The Sun, if viewed from any other system in the 
universe, would appear as a fixed star does to us. 



NERCVftY. 7 

CHAPTER III. 

MERCURY. 

Mercury* is the smallest of the interior planets, 
and the nearest planet to the sun. His diameter is 
above one third of the diameter of our earth, or about 
3,000 miles. He revolves about the sun in 87 days, 
23 hours, and j, at the distance of about 37,000,000 
of miles from that luminary ; moving in his orbit at 
the amazing rate of above 112,000 miles an hour, or 
31 miles in a second. 

By the term orbit is meant, the path described by a 
planet in its course round the sun, or by a moon round 
its primary planet. 

For an illustration of the planets' orbits, see the Frontispiece. 

Some authorities make Mercury's diameter 200 miles more, and 
others as much less. His mean distance from the sun is to that of the 
earth from the sun, as 387 to 1,000, or considerably more than one-third. 

Though small, he has a bright appearance, with a 

light tint of blue ; he never departs much more than 

30° from the sun, and on that account is usually hid in 

the splendour of that luminary. 

The sun's diameter will appear, if viewed from Mercury, nearly 
three times as large as from the earth. And the sun's light and heat at 
Mercury, have been calculated at above seven times those of the earth: 
upon the supposition that the materials of which Mercury is composed, 
are of the same nature as those of our globe.t 

Mercury's diurnal motion, or time of rotation on his 



* Mercury, was considered, mythologically, as the messenger of the 
gods. 

t These decrees of heat and light are presumed, upon the long and 
generally received opinion, that the sun is a globe of fire. 



8 VENUS, 

axis is 24 hours and 5 minutes, and the inclination of 

his axis to his orbit is very small. 

Mercury changes his phases in a manner similar to 

the moon, according as he is stationed with regard to 

the earth and sun. 

This planet, however, never appears to us quite full ; because, when 
his bright side is turned fully to us, he is lost in the sun's beams. From 
these different phases it is clear that he does not shine by his owti light ; 
for if so, he would appear always round. 

As the orbit of this planet is between the earth's or- 
bit and the sun, he will at times appear to pass exactly 
between them ; and this appearance is denominated ike 
transit of Mercury over the surCs disc : the planet then 
appearing like a black spot moving across the face of 
the sun. 

As the planes of the earth and Mercury's orbits are not coincident, 
this appearance does not often happen. The last transit happened, Nov. 
5, 1822 ; a second will happen, May 5, 1832 ; and another, Nov. 7, 1835. 

VENUS. 

Venus is the second planet from the sun, and is 
easily distinguished by her superior brightness and 
whiteness. Her mean distance from that luminary is 
about 69,000,000 of miles, and she completes her an- 
nual revolution in less than 225 days, with a rotation 
about her axis in 24 hours nearly. 

Hence, the length of her year is not quite trwo-thirds of ours. Bian- 
chini makes a complete rotation on her axis to be 24 hours 8 minutes ; but 
the Cassinis, 23 hours 20 minutes ; and Schroeter 23 hours 21 minutes. 

The circumference of her orbit is at least 433,000,000 of miles. 

Her magnitude is nearly the same as that of the earth ; 
her diameter being about 7,900 miles ; and she moves 
in her orbit at the rate of 75,000 miles in an hour. 



VENUS. 9 

The quantity of light and heat which this planet re- 
ceives from the sun, may be supposed to be double that 
of the earth. Her lustre is so great that she has been 
seen in the day-time, when the sun shines ; and at night 
■he usually projects a real shade. 

Venus, when viewed through a telescope, is neve 
seen to shine with a bright full face. But she ha 
phases changing like the moon ; for sometimes she ap- 
pears gibbous, at others, horned like the new moon, and 
her illumined part is constantly towards the sun ; which 
proves that she moves, not round the earth, but round 
the sun. 

Venus is a morning star when seen by us westward of 
the sun, for then she rises before him ; and an evening 
star when eastward of that luminary, for then she sets 
after him.* She is alternately the one and the other 
about 290 days. 

In her seasons there must be a very considerable 
difference; much more, indeed, than is experienced by 
us. The axis of our earth is inclined only 23J degrees, 
whereas that of Venus inclines about 75 degrees to the 
plane of her orbit. 

Venus appears much larger at sometimes than at others ; and the 
great variations of her apparent diameter demonstrate that, her distance 
from the earth is exceedingly variable. This great inequality, with 
respect to distance between her superior and inferior conjunctions, 
will appear from an inspection of plate 7 fig. 2. See also page 37. 

The orbit of Venus, like that of Mercury, lying be- 
tween the earth and sun, there will happen, at times, 



* When a morning star, she is called, in the language of the poets, 
Phosplwrus, or Lucifer : and Hesperus or Vesper, when an evening star. 

K 2 



10 THE EARTH. 

what is denominated the transit of Venus, or the pass- 
ing of this planet over the sun's disc, in the form of a 
dark round spot : this occurs only twice in about 120 
years. 

One was seen in England in 1639, one in 1761, and one in 1769 : 
only two will happen in the present century, viz. the first in 1874, the 
last in 1882, 

By this phenomena astronomers have been enabled to ascertain the 
distance of the earth from the sun ; and hence the distances of the 
other planets are easily found. Kepler was the first person who predict- 
ed the transits of Venus and Mercury over the sun's disc. And the 
first time Venus was ever seen upon the sun, was on Nov. 16, 1639, 
by our countryman, Mr. Horrox, who was educated at Emanuel Col- 
lege, Cambridge. See a fuller Illustration, Chap. XXXI. 



CHAPTER IV. 

THE EARTH * 

The Earth is the third planet from the sun ; its mean 
distance from him being about 95,000,000 of miles ; its 
diameter is found to be 7,920 miles, and its circum- 
ference to be 24,880 miles. 

Doubtless, to a person placed on the planet Venus, the Earth would 
have as much the appearance of a star as Venus has to us. 

The Earth has two constant motions ; the one about 
its axis, and the other through its orbit round the sun. 
It moves in its orbit at the rate of 68,000 miles an 
hour, which is nearly 20 miles each moment ; and per- 
forms an entire revolution in nearly 365£ days, which 

* The Earth by the ancients was called Terra ; and by astronomers 
Tellvs. 



THE MOON. 11 

is the length of our year. A complete rotation upon its 
axis forms a natural day of 24 hours. 

The more exact time of its annual motion is 3G5 days, 5 houps, 48 
minutes, and 49 seconds. 

Hence the division of time into days and years are prescribed by the 
motions of the Earth ; the former depending upon the rotation of the 
Earth upon its axis ; the latter upon its revolution in its orbit. 

The form of the Earth is not that of an exact globe 

or sphere, but of a spheroid, i. e. a little flatted at the 

poles, having the diameter at the equator, 26 miles 

longer than at the poles. 

The earth was formerly supposed to be a wide extended plane, 
firmly fixed upon something, which it was impossible to describe ; but 
from more recent observations, which will hereafter be explained, it is 
proved to be nearly globular. 

The earth serves as a great satellite to the moon, and 
subject to nearly the same changes as that body under- 
goes. But the Earth appears more than thirteen times 
larger when viewed from the moon, than the moon ap- 
pears to us ; and hence far more luminous. So that 
when it is new moon to our earth, it is a full earth to 
the moon, and the contrary. 

It may, perhaps, be inaccurate to denominate the larger body a sa- 
tellite to the smaller. 

For an illustration of the motions of the Earth, causing the different 
lengths of days and nights, and of the different seasons, see Chap. 
XXV., &c. 

THE MOON. 

The Moon is a satellite to the earth we inhabit, 
about which it revolves in an elliptic orbit, from one 
new moon to another, in 29 days, 12 hours, and 44 mi- 
nutes, very nearly. 

The above is called a synodical month. But the Moon revolves 



12 THE MOON. 

from one point in the heavens to the same point again, in 27 clays, 7 
hours, and 43 minutes, which is called a siderial or periodical month. 
These distinctions will be illustrated in Chap. XXVII. 

The Moon's mean distance from the earth is 240,000 
miles ; and she moves in her orbit at the rate of about 
2,290 miles in an hour. 

Her diameter is 2,160 miles ; and her bulk 
about a fiftieth part of the earth's. She always keeps 
the same side towards the earth ; hence her rotation on 
her axis is performed in the same time as her revolution 
through her orbit ; and hence it appears also that her 
day and night, taken together, are just as long as our 
lunar month ; each being as long as from new moon to 
full moon. 

She accompanies the earth in its annual orbit ; and 
during that period, goes herself nearly thirteen times 
round the earth in an orbit of her own. Hence her 
year does not consist of quite thirty days. The different 
forms of increase and decrease which she presents, du- 
ring the time of each revolution, are called the phases 
of the Moon. 

The Moon, like the other planets, is a dark, or opaque 
body, borrowing her light from the sun ; hence, only 
that half which is turned towards him at any time, 
can be fully illuminated ; the opposite half would re- 
main in darkness, if it were not for the light reflected 
from our earth. Therefore, as the light of the Moon, 
visible on the earth, is on that part of her body turned 
towards us, we shall, according to her different posi- 
tions, perceive different degrees of illumination . Hence 
she appears sometimes waning, sometimes horned, then 
half round. If, on the contrary, the moon were a lu- 



THE MOON. 13 

minous body, she would always shine with a full orb, as 
the sun does. 

It has been already noticed that our earth is a satellite to the Moon, 
as is evident soon after the change ; for then her hemisphere towards 
us is illuminated by light which the earth reflects * 

The Moon's axis is almost perpendicular to the plane 
of the ecliptic ; consequently she can have no diversity 
of seasons. 

The inclination of her axis is only 1° 43' 

The shades which appear on the face of the Moon, 
are found, when viewed through a telescope, to result 
from the diversity of mountains and valleys. 

Some of the mountains in the Moon were formerly supposed to be 
five miles high ; but Dr. Herschel has determined with greater precision 
than former astronomers, that very few of them exceed half a mile in 
perpendicular elevation. He has also observed several volcanoes in 
the Moon, emitting fire, as those on the earth do. Two of them ap- 
peared to him nearly extinct, but a third showed an actual eruption of 
fire, or luminous matter. When the Moon is either horned or gibbous, 
the irregularity of her surface is. clearly discerned by the border of the 
Moon appearing indented or jagged, especially about the edge of the 
illumined part. See plate 18. 

The Moon at her conjunction is invisible to us : her 
first appearance afterwards is called new moon ; in op- 
position her whole disc is enlightened ; it is then called 
full moon. 

One remarkable circumstance relating to the Moon is, that the hemi- 
sphere next the earth, can never be really dark ; for when it is turned 
from the sun, it continues illuminated by light reflected from the earth, 
in the same manner as w r e are enlightened by a full moon. But the other 
hemisphere of the Moon has a fortnight's light, and a fortnight's dark- 
ness by turns. 

* The Greeks gave to the Moon the name of Selene. 



14 MARS. 

The sun and stars rise and set to the inhabitants of 

the Moon, in a manner similar to what they do to us; 

and we are led to conclude that, like the earth, the 

Moon is also inhabited. 

No large seas or tracts of water have been observed in the Moon 
by Dr. Herschel, or any other astronomer, nor did he notice any indi- 
cations of a Lunar atmosphere. Recent observations, however, on the 
occultations of Jupiter and Venus by the Moon, render it highly proba- 
ble that the Moon, as well as the earth, is surrounded by an atmosphere. 
On April 5th, 1824, Mr. Ramage, of Aberdeen, Captain Ross, of the 
Navy, and Mr. Cornfield, at Northampton, observed, with excellent 
telescopes, the occultalion of Jupiter, and to all of them the disc of the 
planet appeared distorted when it approached the limb of the Moon ; and 
Mr. Cornfield, at Clapham, on Oct. 30th, 1825, observed, on the emer- 
sion of Saturn from behind the dark limb of the Moon, first the disc 
of the planet, and then the eastern extremity of the ring decidedly flat- 
tened, a phenomena perfectly analogous to what would be produced 
by refraction, and therefore rendering it highly probable that the Moon 
is surrounded by an atmosphere. 



CHAPTER V. 

MARS* 

The orbit of Mars is next above that of the earth, 
and he is the first of what are called superior planets. 
He is known in the heavens by a dusky red appearance. 
His distance from the sun is 143,000,000 of miles ; and 
the length of his year is about 687 of our days. 

The cause of his dusky red colour has not been clearly ascertained ; 
whether it arises from a thick atmosphere, or from his being of a na- 
ture the better to reflect the red rays of light. The mean distance of 
Mars from the sun is more than half as far again as that of our earth : 

* The ancients have given the same name to the heathen God of war. 



ASTEROIDS. 15 

that is, if the distance of the earth be considered to consist of 100 parts, 
that of Mars would be 152. 

He moves in his orbit at the rate of 53,000 miles 

in an hour. The diurnal motion of this planet on 

its axis is performed in 24 hours and 39 minutes. His 

diameter is only 4,189 miles ; and owing to his distance 

he is supposed not to possess one half of the light and 

heat which we enjoy. 

The diurnal motion of Mars is ascertained by several spots that are 
seen in him, when he is in that part of his orbit which is opposite to the 
sun and earth. Dr. Hook first discovered them, and Cassini and ller- 
schel have from them, at length, determined his motion on his axis. 

Though Mars, when viewed through a telescope, ap- 
pears mostly full, yet he is seen, at times, to increase 
and decrease somewhat like the moon ; with this excep- 
tion, that he is never horned. Hence we infer that he 
shines not by his own light ;^-that his orbit exceeds 
that of the earth, and includes both the earth and the 
sun. No satellites or moons have been discovered to 
attend on Mars. See plate 5. 

Mars, when in the part of the heavens opposite to the sun, appears 
about five times larger than when he is near the sun; which proves 
that he must be much nearer to the earth in one situation than in an- 
other. This will receive illustration by an inspection of plate 7, fig. 
2, where the great inequality, with respect to distance, is seen between 
his opposition and conjunction. It is evident, also, that it is not the earth 
that is in the centre of his motion, but the sun. 

ASTEROIDS. 

Between the orbits of Mars and Jupiter, four small 
planets, called Asteroids, have lately been discovered, 
viz. Vesta, Ceres, Pallas, and Juno. 

Vesta, though the last discovered, is nearer to Mars 
than the other three : its mean distance from the sun 



16 ASTEROIDS. 

being 225,000,000 miles ; and the revolution through 
its orbit is performed in 1,320 of our days. Its incli- 
nation to the ecliptic is 1\ degrees, being rather more 
than that of Mercury. The size of this planet is not 
yet ascertained. 

Vesta was discovered by Dr. Olbers, a physician of Bremen, in Ger- 
many, early in 1807. This planet is much smaller than our moon. 

Ceres's mean distance from the sun is 263,000,000 
miles, not quite three times that of the earth. Its 
time of revolution is 4 years, 7 months, and 10 days ; 
its diameter 1,582 miles, and it is inclined to the eclip- 
tic in an angle of about 10£ degrees. 

Ceres was discovered by M. Piazzi, of Palermo, in Sicily, Janu- 
ary 1, 1801. 

Pallas' s mean distance from the sun is nearly the 
same as that of Ceres ; not quite three times that of 
the earth, namely 263,000,000 miles. Its revolution 
is made in about four years. Its orbit is inclined to 
the ecliptic, in an angle of about 34£ degrees ; and its 
diameter is 2,280 miles. 

Pallas was discovered by Dr. Olbers, in March 1802. 

Juno's mean distance from the sun is 252,000,000 
miles ; and its size nearly equal to that of Ceres. It 
revolves round the sun in 4 years and 4 months ; and 
its diameter is 1,393 miles. Its inclination to the 
ecliptic is 13 degrees ; and it appears like a star of the 
eighth magnitude. 

Juno was discovered by M. Harding of Lilienthal, new Bremen, 
Sept. 1st, 1804. 



page L< 



Plate 8 




JUPITER. 17 

CHAPTER VI. 

JUPITER* 

Jupiter's orbit lies between those of Mars and Sa- 
turn ; he is the largest of all the planets, and is easily 
distinguished by his peculiar magnitude and brilliancy. 
He exceeds all the planets in brightness, except some- 
times Venus. The distance of Jupiter from the sun 
is estimated at more than 490,000,000 of miles. 

Jupiter's mean distance from the sun is 52 of those parts of which 
the earth's distance is 10 ; hence, he is full five times farther from the 
sun than the earth is. And if It be admitted that light and heat dimin- 
ish in proportion as the squares of the distances increase, the inhabit- 
ants of Jupiter receive but a 25th part of the sun's light and heat that 
we enjoy. See plate IB. 

Jupiter's diameter is more than ten times that of the 
earth, it being 89,170 miles ; and therefore his magni- 
tude is about 1,300 times that of the earth. 

His year is nearly equal to 12 of ours, for he makes 
one revolution round the sun in 4,332 days and a half: 
consequently he travels at the rate of more than 25,000 
miles in an hour. 

Jupiter revolves on his axis, which is perpendicular 
to its orbit, in less than 10 hours, at the amazing rate 
of 26,000 miles an hour, a velocity 25 times greater 
than the earth's. Hence, by this swift diurnal rota- 
tion, his equatorial diameter is 6,000 miles greater than 
his polar diameter. And as the variety in the seasons 
of a planet depends upon the inclination of its axis to 
its orbit, and as Jupiter has no inclination, there can be 



* The great heathen deity is characterized by this name. 

C 



18 jupiter's satellites. 

no difference in his seasons, nor any variation in the 
length of his clays and nights. 

Jupiter's days and nights are always 5 hours each, in length, and 
about his equator there is perpetual summer ; and an everlasting win- 
ter in his polar regions. If the axis of this planet were inclined to his 
orbit any considerable number of degrees, it might be less habitable 
about the poles ; for then each pole would be nearly six years together 
in darkness. 

When viewed through a telescope, Jupiter is per- 
ceived to be surrounded by faint substances, called 
zones or belts. These belts are generally parallel to 
its equator, and which is very nearly parallel to the 
ecliptic. They are subject to great variations both in 
number and figure. Sometimes eight have been seen at 
once ; sometimes only one. Sometimes they continue 
for three months with little or no variation, and some- 
times a new belt has been seen in less than two hours. 
From their being subject to such changes, it is inferred 
that they do not adhere to the body of Jupiter, but ex- 
ist in his atmosphere. 

This planet, even on the most careless view through 
a good telescope, appears to be oval, the longer diame- 
ter being parallel to the direction of the belts. 

Professor Struve of Dorpat, by the most accurate ad- 
measurements, has determined the proportion between 
the greatest and least diameters to be as 1,371, to 1,000. 

Jupiter's Satellites. 

This planet has four satellites revolving about him 
at different distances, and in different periods of time ; 
the nearest making a revolution in less than two days, 
and the most distant in little more than sixteen: hence 



JUPITER'S SATELLITES. 19 

their relative situation changes every instant. Conse- 
quently, these satellites, like our moon, are subject to 
be eclipsed, and their eclipses arc of considerable im- 
portance to astronomers. They were first discovered 
by Galileo in 1G10. 

Galileo took them, at first, for telescopic stars ; but farther observa- 
tion convinced him and others that they were planetary bodies. The 
periodical time of the first satellite is in about one day and 18 hours, 
the second in 3 days 13 hours ; the third in 7 days 3 hours ; and the fourth 
in 1G days 16 hours. 

The angles under which the satellites appear at the 
mean distance of the planet from the earth, have been 
determined with great precision by Struve, to be first, 
1,018", second 0,914", third 1,492", fourth 1,277". 
These numbers represent also the proportions of the 
diameters of the satellites. It hence appears, that the 
second is the smallest, the third the largest, and the 
fourth larger than the first. 

By means of the eclipses of Jupiter's satellites, a 
method has been obtained for determining the longi- 
tude of places, with facility and some accuracy; and 
also for demonstrating that the motion of light is pro- 
gressive, and not instantaneous as was once supposed. 

The velocity of light is more than a million of times 
greater than of a ball issuing from a cannon. Rays of 
light come from the sun to the earth in less than 8 
minutes; which is at the rate of about 12,000,000 of 
miles in a minute. 



20 SATELLITES OF SATURN. 

CHAPTER VII. 

SATURN* 

Saturn till of late years was esteemed the sixth and 

the most remote planet of the solar system. He shines 

with a pale dead leaden light. His mean distance 

from the sun is about 9J times farther off than that 

of the earth, being nearly 900,000,000 of miles. Of 

course the light and heat he derives from the sun, are 

about 90 times less than at the earth. 

It has been calculated, however, that the light of the sun at Saturn 
is 500 times greater than that which we enjoy from our full moon. 
While our day-light is calculated to exceed that of our full moon 90,000 
times. 

The diameter of Saturn is nearly 80,000 miles, and 
his magnitude almost a thousand times that of the 
earth. He performs his revolution in his orbit round 
the sun in less than 30 of our years (10,759 days,) 
consequently he must travel nearly 21,000 miles an 
hour. He revolves about his axis in 12 hours and 13 J 
minutes. 

Cassini and others attempted, but without success, to determine the 
rotation of Saturn about his axis ; but Dr. Herschel's observations have 
at length ascertained it. The Phil. Trans, of 1794 say 10*» 16' 0"4 ; but 
later accounts say 12 h 13£'. 

Satellites of Saturn. 

Saturn is attended by seven Satellites or Moons, 
whose periodical times differ very much. The one 
nearest to him performs a revolution round the primary 

* This name is given to the supposed father of the Heathen gods. 






**■* afdU I'h. 



\ Saturn 




-$ Vr>- 




o 



% Venus 



o 







sj # Mercury 




% Jupiter 



RING. 21 

planet in 22 hours and a half; and that which is most 

remote takes 79 days 7 hours. 

The last Satellite is known to turn on its axis, and in its rotation to 
be subject to the same law which our moon obeys \ that is, ii revolves 
on its axis in the same time in which it revolves about the planet. 

Saturn's Ring. 

Saturn is also encompassed with a kind of Ring, 
or, according to Dr. Ilerschel, with two concentric 
rings, situated in one plane, which is not much inclin- 
ed to the equator of the planet. They may probably be 
of considerable use in reflecting the light of the sun to 
him. See plate. 

From numerous observations it has been concluded, that the near- 
est is 21,000 miles distant from Saturn, and that the breadth of the inner 
ring is 20,000 miles ; that of the outer ring 7,200 miles; and the vacant 
space between the two rings 2,839 miles. 

Dr. Herschel conjectures that it is no less solid than the planet itself ; 
and he has found that it casts a strong shadow upon the planet. The 
light of the ring he has observed brighter than that of the planet ; for the 
ring appears sufficiently bright for observation at times, when the tele- 
scope scarcely affords light enough to give a fair view of Saturn. 

Professor Struve has made some interesting obser- 
vations on this planet, with a superb refracting teles- 
cope. — The results of his admeasurements are, that at 
the mean distance of the planet, 

// 
The external diameter of the external ring is 40.215 

The internal diameter of the external ring is 35.395 

The external diameter of the internal ring is 34.579 

The internal diameter of the internal ring is 26.748 

The equatorial diameter of Saturn is . . 18.045 

The breadth of the external ring is . . . 2.410 

The breadth of the chasm between the rings is 0.408 

c2 



22 THE GEORGIUM SIDUS. 

The breadth of the internal ring is . . . . 3.915 
The distance of the ring from Saturn is . , 4.352 

He adds, " it is remarkable that the outer ring is much 
less brilliant than the inner. The inner one too, to- 
wards the planet, seems less distinctly marked, and to 
grow fainter ; so that I am inclined to think that the 
inner edge is less regular than the others." 

The Ring has a rotation about its axis, or, which is 
the same thing, revolves about the planet, in the same 
time that Saturn turns round on his axis. 



CHAPTER VIII. 

URANUS, OR HERSCHEL. 

This is the most remote planet yet discovered in our 
Solar system. He appears of a bluish white colour, 
and can rarely be seen but by means of a telescope. 

He may be best perceived, by the naked eye, in a very clear night 
when the moon is absent. 

To Dr. Herschel the world is indebted for the discovery of this planet, 
on the 13th of March, 1781. The Doctor, in honour of George III. 
king of England, named it the Georgium Sidus, (or Georgian Star,) 
though by astronomers it is called the Herschel, in testimony of re- 
spect to the discoverer. American astronomers call it Uranus. 

The distance of this planet from the sun is more than 
1,800,000,000 miles ; or about nineteen times that of 
the earth. 

The distance given by some authors, is 1,812,000,000 miles. The 
light and heat which he derives from the sun, are supposed to be about 
the 361st part of those at our earth (for the square of 19 is 361 ; which 



PROPORTIONAL MAGNITUDE, &C OF PLANETS. L\3 

see explained in a future chapter)— that is, about equal to the effect of 
849 of our full moons. 

He performs his annual revolution in 3,069 days, or 
about 84 of our years ; consequently he must travel at 
the rate of 16,000 miles an hour. 

The time of his completing a revolution has been ascertained by a 
series of observations. When first discovered in March 1781, he was 
in Gemini ; and in August 1803, he had advanced to 11° of Libra; or 
through more than a iburth part of his orbit. 

His diameter is found to be 35,865 English miles ; 
but his diurnal rotation has not yet been discovered. 

The Herschel's Satellites. 

The Herschel, or Uranus has six Satel- 
lites ; the one nearest the planet performs his revolution 
round the primary in less than six days; and that which 
is the most remote in rather more than 107 days and a 
half. 

Though the light of these Satellites or Moons is, as Dr. Herschel 
observes, extremely faint, yet they are, probably, of great benefit to the 
inhabitants of that planet ; for it is reasonable to conclude that there is 
scarcely any part of his orb but what is constantly enlightened by one 
or other of them. 

The proportional Magnitude and Distance of the 
Planets. 

The Earth is fourteen times as large as Mercury ; — very little larger 
than Venus ; — three times as large as Mars ; more than a million times 
as large as Pallas. But Jupiter is more than fourteen hundred times as 
large as the Earth. Saturn above a thousand times as large, exclusive 
of his ring ; and the Georgian eighty times as large. 

As the distances of the planets when given in miles, are such a 
burthen to the memory as seldom to be retained, astronomers often ex- 
press their mean distances in a shorter way, by supposing the distance 
of the earth from the sun to be divided into ten parts. Mercury may 



24 COMETS. 

then be estimated at nearly four of such parts from the sun. Venus at 
seven, the Earth at ten, Mars at full fifteen, Jupiter at fifty-two ; Saturn 
at ninety-five, and the Georgian one hundred and ninety parts. [See 
the scale on the frontispiece.] These are calculated by multiplying the 
respective distances of the planets by 10, and dividing by 95, the mean 
distance of the earth from the sun. For the relative magnitudes of the 
planets see plate 3. 



CHAPTER IX. 



COMETS. 



Comets, like the orbs already mentioned, are sup- 
posed to be planetary bodies forming a part of our sys- 
tem; for, like the planets, they revolve round the sun ; 
not, indeed, in orbits nearly circular, but in very dif- 
ferent directions, and in extremely long elliptic curves, 
having the sun in one of their foci ; approaching some- 
times near the sun, at others stretching far beyond the 
orbit of the remotest planet. The periods of their revo- 
lutions are so long that only three are known with any 
degree of certainty. 

Some suppose them not adapted for the habitation of animated be- 
ings, on account of the great extremes of heat and cold, to which, in 
their course, they appear to be subject. 

The name of Comet is derived from Cometa, " hairy ;" 
because Comets appear with long tails, somewhat re- 
sembling hair. This appearance is supposed to be no- 
thing more than vapour arising from the body in aline 
opposite to the sun; some indeed have been seen with- 
out such appendage, and as round as the regular planets. 
The knowledge, however, which we have of Comets, is 



OOMBTS. 25 

very imperfect, as they afford but few observations on 
which to ground conjecture. 

By common people they nre called blazittg stars, and by some they 
are thought to be portentous; presaging some extraordinary event But 
they can have no such tendency, nor can there be any apprehension 
that they can injure the earth we inhabit, by coming into contact. Even 
the tail of the Comet cannot come near our atmosphere, unless it should 
be at its inferior conjunction very nearly at the time when it is in its 
node ; circumstances so extremely unlikely, that there are some mil- 
lions to one against such a conjunction. 

It was thought that the periods of three of the Comets had been dis- 
tinctly ascertained ; the first of these appeared in 1531, 1607, and 1682, 
and it was expected to return every 75th year ; and one did appear in 
1758, which was supposed to be the same. 

The second of them appeared in 1532 and 1661, and was again 
expected in 1789, but in this the astronomers were disappointed. 

The third was that which appeared in 1680, and its period being es- 
timated at 575 years, cannot, upon that supposition, return till 2255. 
This Comet, at its greatest distance, is 11,200,000,000 of miles from the 
sun ; and its least distance from the sun's centre was but 490,000 miles ; 
in this part of its orbit it travelled at the rate of 880,000 miles in an hour. 

Comets differ much in their magnitude, though most 
of those which have been observed are less than the 
moon ; but their dimensions are not determined with 
accuracy. 

The head of the Comet of 1807 was ascertained to 
be about 538 miles in diameter; and that of 1811, 
about the size of the moon. 

According to Sir Isaac Newton, comets are of an 
opaque nature, and consist of a very compact, durable, 
and solid substance, capable of bearing exceedingly 
great degrees of heat and cold. The Comet seen by 
him in 1680, was observed to approach so near the sun 
that its heat was estimated by him to be 2,000 times 
greater than that of red hot iron. And it has been said 



26 THE FIXED STARS. 

that a globe of red hot iron as large as our globe would 
scarcely cool in 50,000 years. 

Notwithstanding the above supposition the appearance of the two 
brilliant Comets, of late, seems to overturn that theory. Of that in 1807, 
Dr. Herschel says, we are authorized to conclude that the body of the 
Comet, on its surface is self 'luminous, from whatever cause this quality 
may be derived. The vivacity of the light of the Comet, also, had a 
much greater resemblance to the radiance of a star, than to the mild 
reflection of the sun's beams upon the moon. 

Comets consist (according to modern observation) of the nucleus, the 
head, the coma, and the tail. The nucleus is a small and brilliant part 
in the centre ; the head includes all the very bright surrounding light; 
the coma is the hairy appearance surrounding the head ; and the tail, 
which is of great length, is supposed to consist of radiant matter, such 
as that of the aurora borealis. 

The tail of the Comet in 1807, was ascertained to be more than 
9,000,000 of miles in length ; and that in 1811, to be full 33,000,000 in 
length. The distance of this Comet from the sun was 95,000,000 ot 
miles, and from the earth upwards of 142,000,000 of miles. 



CHAPTER X. 

THE FIXED STARS. 

All the heavenly bodies beyond our system are 
called Fixed Stars, because, except some few, they 
never appear to move or to change their places, with 
regard to each other, as the planets do. As they are 
placed at immense distances from our system, they 
must be bodies of great magnitude, and doubtless shine 
by their own light. They are probably suns, like our 
sun, to different systems of planets : each fixed star 
being supposed to be the centre of its own system. 

That the fixed stars shine by their own light is concluded ; being at 
such vast distances from the sun, they could not possibly receive from 
him so strong a light as they shine with. So great is their distance 






I'httr w 



■ '/>/<' llfft'S 




Jupiter 



■ hi fiiter 



?% 




* Jloon 



Mars 




Mars 




W 



Mars 



Tin: fixed stars. 27 

thai though the orbit of the earth is tu ice 95,000,000 of miles across, and 
we are consequently 190,000,000 of miles nearer to some^stara atone 
time than we are at another, yet the stars always appear in the same 
places, and with the same magnitude. See plate IV. fig. 2. Let * * * 
represent the fixed stars, and A B C D, the earth's annual course ; then 
will the earth in that part of its orbit at B, be 190,000,000 of miles nearer 
to the fixed stars, than when at D. 

The distance of Sinus, or the Dog-star, the nearest 
of the fixed stars, cannot be less than two millions of 
millions of miles. A cannon ball flying from that star 
at the rate of 400 miles an hour, would not reach us in 
570,000 years. 

Professor Vince says, " the nearest fixed star cannot be less than 
400,000 times farther from us than the sun is." Hence 400,000, multi- 
plied by 95,000,000, give 38 millions of millions of miles for the near- 
est fixed star. 

Dr. Herschcl says, that several of the fixed stars revolve on their 
axes. 

The fixed stars, then, are most probably suns, which, 
like our sun, serve to enlighten, warm, and sustain 
other systems of planets, and their dependent satellites. 

They are usually classed into six magnitudes, which 
include all that can be seen without a telescope ; the 
largest are called stars of the first magnitude, and the 
smallest, those of the sixth. There are seldom so many 
as a thousand visible at one time, to the naked eye, 
even in a clear star-light night. 

The number of stars appears to us at times innumerable ; but this is 
a deception, occasioned from their being observed by us in a confused 
manner, or by the refraction and reflection of the rays of light, passing 
from them through our atmosphere. 

Many of the fixed stars, which to the naked eye ap- 
pear as single stars, are found to consist of two, and 
some even of three, or more. — Not that they are really 



28 THE FIXED STARS. 

double or treble, but they are stars at different dis- 
tances, which appear nearly in a right line. There are 
also clusters of stars, called nebula : the most remark- 
able of these is, that broad zone, called the Milky way. 
In this bright track, Dr. Herschel has seen 116,000 
stars pass over the field of his telescope, in a quarter of 
an hour. 

The Magellanic clouds, near the south pole, which resemble two 
whitish spots in the heavens, are of the order of nebula, and are well 
known to sailors. 

Since the introduction of telescopes, the number of fixed stars has 
been considered as immense ; and by the greater perfection of our 
glasses, still more stars are discovered ; so that there appear to be no 
bounds to their number, or to the extent of the universe. 

There are two methods of discovering which are 
planets, and which are fixed stars : the first is by their 
twinkling or not ; for every fixed star twinkles, but a 
planet does not. The second is by the nature of their 
motions : they all, indeed, appear to rise and set ; but, 
besides that, the planets have a motion from one part 
of the heavens to another, sometimes among the fixed 
stars in one constellation, at other times among those 
of another ; whereas the fixed stars keep constantly the 
same relative distance from each other. 

Many conjectures have been offered as to the cause of the twinkling 
of the fixed stars; perhaps it may be the unequal refraction of light, in 
consequence of inequalities and undulations in the almosphere. 

Several stars mentioned by ancient astronomers are 
not now to be found, and several are now observed 
which do not appear in their catalogues. 

The most ancient observations of a new star is that by Hipparchus, 



THE FIXED STARS. 29 

about 120 years before Christ. Some others have been noticed in later 
times ; but the first new star we have any accurate account of, is that 
which was discovered by Cornelius Gemma, in 1572, in the Chair of 
Cassiopeia. It exceeded Sirius in brightness, and was seen at mid-day. 
It first appeared larger than Jupiter, but it gradually decayed ; after six- 
teen months it entirely disappeared. 

Some fixed stars have been noticed alternately to ap- 
pear and disappear, and others have been subject to 
great periodical variations in their magnitudes. 

In 1600, a changeable star was discovered by W. Jansenius, in the 
neck of the Swan, which appeared visible for many years ; but from 1640 
to 1650 was invisible. It was seen again in 1655, increased till 1660, 
then grew T less, and disappeared. In 1665 re-appeared ; disappeared in 
1681. In 1715, it appeared of the sixth magnitude, as it is seen at present. 

To mention one more instance, among many, £ Lyras, was discovered 
by Mr. Goodrich , to be subject to aperiodic variation. It completes all 
its phases in 12 days, 19 hours, during which time it undergoes the fol- 
lowing changes : 1. It is of the third magnitude for about two days. 
2. It diminishes in about 1£ day. 3. It is between the fourth and fifth 
magnitude for less than a day. 4. It increases in about two days. 5. It 
is of the third magnitude for about 3 days. 6. It diminishes in about one 
day. 7. It is something larger than the fourth magnitude for a little less 
than a day. 8. It increases in about one day and three quarters to the 
first point, and so completes a whole period. See Phil. Trans. 1785. 

In whatever part of the universe we are, we appear 
to be in the centre of a concave ; that is, a hollow sphere, 
where all remote objects appear at equal distances from 
us ; so that, whether we are on the planet Venus, or on 
the earth, or on any planet or star in the universe, the 
effect in this particular would be the same. 

As a proof of this, the sun, moon, and stars, appear 
at equal distances ; whereas the sun (as has been men- 
tioned) is 400 times farther off than the moon, and the 
fixed stars at least 200,000 times farther from us than 
the sun. 

If transplanted to a planet of any other system, sup- 

D 



30 CONSTELLATIONS. 

pose to one belonging to Sirius ; then Sirius, which now 

appears only as a star, would prove a sun. Our sun 

would then appear as a star, and the earth, with all the 

other planets, would be invisible. 

The vulgar error, that all these stars were placed in the heavens only 
to afford us light, must be erroneous, since thousands of them are invisi- 
ble to us without the help of a telescope, and we receive more light 
from the moon, than from all the stars together. 



CHAPTER XL 

CONSTELLATIONS. 

The ancients, in reducing astronomy to a science, 

formed the fixed stars into constellations, or collections 

of stars, and represented them by animals, and other 

figures, according to the ideas which the dispositions 

of the stars suggested. 

This arrangement took place very early ; for some kind of division 
must have been suggested by necessity, in order that astronomers might 
describe any particular star so as to be understood. Neither, without 
some such division, could the situation of the planets have been point- 
ed out, as they are continually changing their places. We find mention 
made of Orion and Pleiades by Job. Homer and Hesiod also make 
mention of some of them ; but Aratus enumerates almost all the an- 
cient ones. 

The number of the ancient constellations was about 
fifty, but the present number upon the globe is eighty. 

The heavens are usually distinguished by three re- 
gions, called the Northern and Southern hemispheres, 
and the Zodiac. The number of the constellations, 
in the northern hemisphere, is 36 ; in the southern, 32 ; 
and in the zodiac, 12. Stars not comprehended in any 
of these, are called unformed stars. 



constellations. 31 

North kkn Constellations. 

number of stars. 

Ursa Minor. The Little Bear 24 

Draco. The Dragon 80 

Cepheus 35 

Lacerta. The Lizard 16 

Cassiopeia. The Lady in her Chair .... 55 

Perseus ) 

i 59 

Caput Medusae. Medusa's Head ) 

Camelopardalus. The Camelopard 58 

Lynx. The Lynx 44 

Ursa Major. The Great Bear 87 

Cor Caroli. Charles's Heart 

Leo Minor. The little Lion . 53 

Coma Berenices. Berenice's Hair 43 

Asterion and Chara. The Greyhound .... 25 

Bootes 54 

Corona Borealis. The Northern Crown ... 21 

Hercules. Hercules kneeling 113 

Cerberus. The Three Headed Dog .... 9 

Lyra. The Harp 21 

Cygnus. The Swan ......... 81 

Velpecula et Anser. The Fox and Goose . . 35 

Sagitta. The Arrow 18 

Delphinus. The Dolphin ... ^ .... 18 

Pegasus. The Flying Horse 89 

Andromeda 66 

Triangulum Boreale. The Northern Triangle . 16 
Musca. The Fly 

Auriga. The Wagonner 66 

Mons Maenalus. The Hill Maenalus 



32 CONSTELLATIONS. 

NUMBER OF STARS. 

Serpens. The Serpent 64 

Serpentarius. The Serpent Bearer 74 

Scutum Sobieski. Sobieski's Shield .... 8 
Taurus Poniatowski. Poniatowski's Bull 

Antinoiis 34 

Aquila. The Eagle 12 

Equulus. The Colt 10 

The Southern Constellations. 

Piscis Australis. The Southern Fish .... 24 

Cetus. The Whale 97 

Eridanus. The River Po 84 

Orion 78 

Lepus. The Hare 19 

Canis Major. The Great Dog ...... 31 

Monoceros. The Unicorn 39 

Canis Minor. The Little Dog 14 

Hydra. The Hydra 60 

Sextans. The Sextant 41 

Crater. The Cup 31 

Corvus. The Crow 9 

Argo Navis. The Ship Argo 64 

Crux. The Cross 

Centaurus. The Centaur 35 

Lupus. The Wolf 24 

Ara. The Altar 9 

Corona Australis. The Southern Crown ... 12 

Columba Noachi. Noah's Dove 10 

Robur Carolinum. The Royal Oak .... 12 

Apis. The Bee 4 






■>'_• 



/•'/if. / 



I •hit,' / 







Fiq. 



^ 




CONSTELLATIONS. 33 

NUMBER OF STARS. 

Triangulum Auslralc. The South Triangle . . 5 

A pus. The Bird of Paradise 11 

Pavo. The Peacock 14 

Indus. The Indian 12 

Grus. The Crane 13 

Phoenix. The Phoenix 14 

Toucon. The American Goose 9 

Hydras. The Water Snake 10 

Dorado. The Sword Fish 6 

Piscis Volans. The Flying Fish 8 

Chamaeleon. The Cameleon 10 

The Zodiacal Constellations. 

Aries. The Ram 66 

Taurus. The Bull 141 

Gemini. The Twins 85 

Cancer. The Crab 83 

Leo. The Lion 95 

Virgo. The Virgin 110 

Libra. The Balance . 51 

Scorpio. The Scorpion 44 

Sagittarius. The Archer 69 

Capricornus. The Goat 51 

Aquarius. The Waterman 108 

Pisces. The fishes . . . . . . . . . .113 

Some of the principal fixed stars are distinguished by 
particular names, as Regulus, Arcturus, Sirius, &c. ; 
others are denoted by the letters of the Greek alphabet : 
the first letter being put to the greatest star in each 
constellation ; the second letter to the next greatest, and 

d 2 



34 DIFFERENT SYSTEMS. 

so on ; and when any more letters are wanted, the Italic 

letters are generally used. 

By this contrivance the place of any particular star in the heavens 
may be found, with the greatest ease and precision. 



CHAPTER XII. 

DIFFERENT SYSTEMS. 

The system we have been describing, and which is 
now universally received, is called the Copernican. It 
was formerly taught by Pythagoras, a Greek philoso- 
pher, born in the island of Samos, 590 years before 
Christ, and Philolaus, his disciple, finding it impossible 
any other way to give a consistent account of the hea- 
venly motions. 

This system, however, was so extremely opposite to 
all the prejudices of sense and opinion, that it never 
made any great progress in the ancient world till re- 
vived by Copernicus. 

Ptolemy, an Egyptian philosopher, who flourished 
130 years after Christ, supposed at first that the earth 
was perfectly at rest near the centre ; and that all the 
other bodies, namely, the sun, moon, planets, comets 
and fixed stars, revolved about it in circles every day. 
But as their retrograde motions and stationary appear- 
ances could not thus be solved, he afterwards supposed 
them to revolve in epicycloids. 

Epicycloids are curves generated by the revolution of the periphery 
of a circle along the concave or convex parts of another circle. 

The full illustration of this motion may exceed the present compre- 
hension of the learner, but he may conceive it to be not much unlike 



DIFFERENT SYSTEMS. 35 

the curve line, a, b, c, d, e,/, &c, plate XV. fig. 1. Now it is evident 
that at the points b and c, and also d and e, the planet's motion would 
appear stationary and retrograde from b to c, and from d to e, and at other 
times direct. 

But though this system will not solve the phases of Venus and Mer- 
cury, and for other reasons cannot be true, it was maintained from the 
time of Ptolemy till the revival of learning in the sixteenth century. 

The Egyptians received also the following system : — 
That the earth is immoveable in the centre, about 
which revolve, in order, the Moon, Sun, Mars, Jupiter 
and Saturn ; and about the sun, revolve Mercury and 
Venus. This disposition will account for the phases 
of Mercury and Venus, but not for the apparent motions 
of Mars, Jupiter, and Saturn. 

At length Copernicus, a native of Poland, adopted 
the Pythagorean system, and published it to the world 
in 1530. This doctrine had been so long in obscurity, 
that the restorer of it was considered the inventor. 

Copernicus placed the Sun in the centre of the sys- 
tem, and about it, the other bodies in the following 
order : Mercury, Venus, the Earth, Mars, Jupiter and 
Saturn. 

Europe, however, was still immersed in ignorance, 
and the general ideas of the world were not able to keep 
pace with those of a refined philosophy. This occa- 
sioned Copernicus to have few abettors, but many op- 
ponents. 

Tycho Brahe, a noble Dane, and eminent philoso- 
pher, sensible of the defects of the Ptolemaic system 
but unwilling to acknowledge the motion of the earth, 
endeavoured, about 1586, to establish a new system of 
his own, in which the earth was supposed the centre 
of the sun and moon ; that Mercury, Venus, &c. re- 



36 OF THE MOTION OF THE PLANETS. 

volved about the sun, and that the sun and planets, 

together, turned round the earth in 24 hours. But as 

this proved to be still more absurd than that of Ptolemy, 

it was soon exploded, and gave way to the Copernican, 

or true solar system. 

Some of Tycho's followers, seeing the absurdity of supposing all the 
heavenly bodies daily to revolve about the earth, allowed a rotary mo- 
tion to the earth, in order to account for their diurnal motion, and this 
was called the Semi-Tychonic system. 

Thus the solar system, now adopted, after having 
been taught by Pythagoras, and revived by Copernicus, 
was confirmed by Galileo, Kepler, and Descartes, and 
fully established by Sir Isaac Newton. See Planeta- 
rium, plate 6. 



CHAPTER XIII. 

OF THE MOTIONS OF THE PLANETS: 
DIRECT, STATIONARY, AND RETROGRADE. 

The planets, Mercury, Venus, the Earth, &c. if seen 
from the sun, would appear to pass from star to star, 
through the constellations, in a uniform and regular 
manner. 

But as seen from the earth, they apparently move 
very irregularly ; sometimes they appear to go forward, 
at other times to remain stationary, and then to recede. 

To give some idea of this, suppose yourself placed in the centre of a 
circular course, keeping your eye on the horse while going round ; it 
is evident that he would appear to run round the whole course in a 
regular manner. Again; imagine yourself placed at a considerable 
distance on the outside of the course, and the horse's motions would 



OF THE MOTION OF THE PLANETS. 37 

appear no longer uniform. On the opposite side of the course alone 
would he seem regular : then alone would it appear the same as when 
you stood in the centre. When he approached you, he would scarcely 
seem to move ; in that part of his course next to you, he would move 
in a direction contrary to what he did at first ; and again, when going 
from you, his motion would be scarcely visible. 

When the planets axe farthest from us, their motion 
is said to be direct ; when nearest to us retrograde, 
because they appear to be moving back again ; and 
when either approaching us, or goingjfrom us, we say 
they are stationary, because, if then observed in a line 
with any particular star, they will continue so for a con- 
siderable time ,* now these appearances could not hap- 
pen if they moved round the earth as their centre. See 
plate VII. fig. 1. 

Inferior and Superior Conjunctions of the Planets. 

When Mercury or Venus is nearest to us, that is, 
in a line between us and the sun (see plate VII. fig. 2.) 
we say it is in inferior conjunction ; when farthest 
from us, and the sun is between us and the planet, in 
superior conj unction . 

The superior planets, namely, those whose orbits 
include that of the earth, have alternately a conjunction 
and an opposition ; a conjunction, when the sun is be- 
tween the earth and the planet; and an opposition, 
when the earth is between the sun and the planet, that 
is, when the planet is nearest to us, and appears to be 
opposite to the sun. 

Hence, when a planet is in conjunction, it rises and 
sets nearly with the sun ; but in opposition, it rises 
nearly when the sun sets, and sets when he rises. 



38 THE PLANE OF AN ORBIT, TLA NETS, &C. 

We say nearly, because it cannot be exactly, except when the 
planet is in or near its node ; or, which is the same thing, when the 
sun, earth and planet, are in a right line, which seldom happens. 

As only that side of a planet which is turned to the 
sun can be enlightened by him it is evident, that as 
viewed with a telescope from the earth, its appearance 
must vary ; thus Venus, just before and after her supe- 
rior conjunction, would be seen nearly with a full face ; 
when stationary, she would appear only half enlight- 
ened, like the moon at the first quarter, because an 
equal portion of the bright and dark sides will be turn- 
ed towards us ; the bright parts will be decreasing till 
her inferior conjunction, and then only the dark side 
will be turned towards us, and consequently she will 
be for a short time invisible : by-and-by she will be- 
come again stationary, and appear like the moon at her 
third quarter. 

It is true, both Mercury and Venus may at times be seen even when 
in their inferior conjunctions, but it can be only in their transits, which 
will be explained in a future chapter. 

These appearances refer to the inferior planets only, 
Mercury and Venus. The superior planets always ap- 
pear with nearly a full face. 



CHAPTER XIV. 

THE PLANE OF AN ORBIT, PLANETS, NODES, ETC. 

The earth, as seen from the sun in its periodical re- 
volution, will describe a circle among the stars, which 
astronomers call the ecliptic ; and sometimes the sun's 



THE PLANE OF AN OMIT, PLANETS, &C. 3D 

annual path, because the sun, as seen from the earth, 

always appears in that line. 

Suppose the earth, if seen from the sun, to appear in Cancer, then 
the sun, if viewed from the earth, will appear in Capricorn ; or, if tho 
earth appear in Aries, the sun will appear in Libra. See plate IV. fig. 1. 

By the plane of a circle may be understood that sup- 
posed surface which would lie evenly between every 
part of the circumference. 

Any flat and smooth surface is a plane ; hence the edge of a round 
table may represent the ecliptic, and the surface of the table its plane. 

Though the orbit of the earth and the ecliptic are in 
the same plane, they are not the same thing ; for the 
ecliptic is supposed to extend far beyond that of the 
earth to the fixed stars. 

If the edge of a round table be made to represent the ecliptic, then 
a circle within, drawn from the centre of the table, may represent the 
orbit of the earth, and they will be both in the same plane, though of 
unequal dimensions. 

The orbits of the planets are not in the same plane 
as that of the earth ; in other words, the planets do not 
move in the ecliptic. They are in every revolution 
one-half of their periods a little above the ecliptic, and 
the other half as much below it. This is called the in- 
clination of their orbits (see plate VIII. fig. 1.) where S 
represents the sun ; A B C D the orbit of the earth ; 
and E F G H the orbit of one of the inferior planets, 
suppose of Venus ; the half, F G H, rises above, and the 
other half, H E F, sinks below it, from the points H F, 
which are in a line with the orbit of the earth. 

The dotted line b H F a, is called the line of the 
nodes ; and the points H F, the nodes of the planet. 
The point F is called the ascending node, because the 



40 THE TRANSITS OF ?JERCURY AND VENUS. 

planet is then ascending or rising above the orbit of the 
earth ; or, which is the same thing, above the ecliptic. 
When in H it is descending below it, whence that point 
is called the descending node. 

As the planes of the planets' orbits vary a little from 
each other, so their nodes or intersections are at dif- 
ferent parts of the plane of the ecliptic. 

The dotted line, c d ef may represent the orbit of 
any other planet, and convey some faint idea of the way 
in which they intersect each other. 

Not that we are to suppose, when speaking of the 
plane of the ecliptic, or plane of the earth's orbit, that 
it is a real and visible flat surface ; nor in speaking of 
the orbits of the planets, that we mean solid rings ; for 
the planets perform their revolutions with the utmost 
regularity in unbounded space. 

The Transits of Mercury and Venus. 

If Venus were in her ascending node at F, (plate 
VIII. fig. 1,) when the earth is at a, or in her descend- 
ing node at H, when the earth is at b, she would be in 
a line with the sun, and on the sun's disc she would 
appear a dark round spot passing over it. These ap- 
pearances are called transits; they happen very sel- 
dom, because Venus is very seldom in or near her nodes 
at her inferior conjunctions. 

That there are great variations in the apparent dia- 
meter of Venus may be demonstrated thus : suppose S 
(plate VII. fig. 1.) to be the sun, E the earth in its or- 
bit, and abed, &c. Venus in her's : now it is evident 
that when Venus is at a, between the sun and earth, 



PW 






Telescopic Views of Venus. 




; 






7 




.... 



THE ECLIPTIC, ZODIAC, AND EQUATOR, &C. 4i 

she would, if visible, appear much larger than when 
she is at c in superior conjunction, because so much 
nearer in the former case than in the latter ; being in 
the situation a, but 27,000,000 miles from the earth, 
E; but at e, 163,000,000. 

As Venus passes from a through b c d to e, she may be observed 
by a good telescope to have all the same phrases as the moon has 
in passing from new to full ; therefore when she is at e she is full. 
Also, during her journey from c through/ to g, she will appear to have 
a direct motion in her orbit ; from g to h, and from b to c to be nearly 
statiojiary, but from h to b, her motion, though still really direct, will 
appear to a spectator at £, to be going back again, or retrograde, as was 
shown before. 

Mercury is seen in the same manner, which is a proof 
that their orbits must be within that of the earth. 



CHAPTER XV. 

THE ECLIPTIC, ZODIAC, AND EQUATOR, ETC. 

The Ecliptic is an imaginary great circle in the 
heavens, which the sun appears to describe in the 
course of the year, among the stars. 

The following are the most conspicuous stars that lie 
near to the ecliptic : — The Ram's Horn, called, * Arie- 
tis — Aldebaran, in the Bull's Eye — Castor and Pollux — 
Regulus, or the Cor Leonis — Spica Virginis — Antares, 
or the Scorpion's Heart — also, which lie more distant, 
» Altair, in Aquila — Fomaehaut, in the Fish's Mouth, 
and Pegasus. 

The above nine stars are considered as the most conspicuous near 
the moon's orbit — from these the moon's distance is calculated, and 
hence the tables in the Nautical Almanac are constructed for the use 

E 



42 THE ECLIPTIC, ZODIAC, AND EQUATOR, &C. 

of navigators. The Ecliptic is so called, because all the eclipses must 
necessarily happen in this line, where the sun always is. 

The Ecliptic and Equator, being great circles, must 
bisect, or equally divide each other ; and their inclina- 
tion is called the obliquity of the Ecliptic. Also the 
points where they intersect are called the equinoctial 
points, and the times when the sun comes to these 
points are called the equinoxes. 

The Zodiac is an imaginary broad circle, or belt, 
surrounding the heavens, extending about 8° on each 
side the ecliptic, in which the planets, with the exception 
of Ceres, Pallas, and Juno, constantly revolve. 

The term Zodiac is derived from a Greek word Zw £*axo s ; from £«.<>?, 
" an animal," because each of the twelve signs formerly represented 
some animal ; that which we now call Libra being by the ancients 
reckoned a part of Scorpio. 

For the definitions of degrees, &c. see preliminary definitions. 

The names and characters of the twelve signs, with 
the time of the sun's entrance into them, are as follow : 

1. Aries, T, or the Ram ; March 20th. 

2. Taurus, «, the Bull ; April 20th. 

3. Gemini, n, the Twins ; May 21st 

4. Cancer, 25, the Crab ; June 21st. 

5. Leo, £1, the Lion ; July 23d. 

6. Virgo, ty, the Virgin ; August 23d. 

7. Libra, =£=, the Balance ; September 23d. 

8. Scorpio, "HI, the Scorpion ; October 23d. 

9. Sagittarius, •?, the Archer ; November 22d. 

10. Capricornus, V5, the Goat ; December 21st. 

11. Aquarius, ~, the Waterman ; January 20th. 

12. Pisces, X, the Fishes ; February 19th. 



THE ECLIPTIC, ZODIAC, AND EQUATOR, &C. 43 

Dr. Watt's lines, " The Ram, the Bull," &c. are well known ; but, 
perhaps, to learn the sijjns in the above order will answer a better 
purpose, and be but little extra labour. 

The order of these is according to the motion of the sun. The first 
point of Aries coincides with one of the equinoctial points, and the first 
point of Libra with the other. 

The first six are called northern signs, lying on the 
north side of the equator ; and the last six southern, 
lying on the soutr; side. 

The signs V3, ~, X, T, y, n, are called ascend- 
ing, because the sun approaches our north pole while 
it passes through them ; and 25, £\, ttj 5 ^ it[ ? f y are 
called descending, the sun receding from our pole as it 
passes through them. 

Each of the 12 signs of the Zodiac contains 30 de- 
grees. 

The Equator is either terrestial or celestial. 

The terrestial Equator is an imaginary great cir- 
cle of the earth, perpendicular to its axis; hence the 
axis and poles of the earth are the axis and poles of 
the equator. This circle is equally distant from the 
two poles, and separates the globe into the northern 
and southern hemispheres. 

The celestial Equator, called also the equinoctial, is 
a plane of the terrestial equator extended to the fixed 
stars ; and if the axis of the earth be produced in like 
manner, they will be the poles of the celestial equator. 
And the star nearest to the north pole is called the pole 
star, as P. P. fig. 2, plate II. 



44 THE EPHEMERIS. 



OF THE EPHEMERIS, 

The Astronomical Ephemeris being frequently alluded to in 
the use of the globes and the study of astronomy, a short ex- 
planation of the astronomical part of the only work of this kind 
published in this country, viz. the American Almanac, may be 
acceptable, taking, for example, that for the current year, 1832. 

The first thirty -five pages, which are occupied by the relations 
of the planets, the time of the entrance of the Sun into the signs 
of the Zodiac, the length of each of the four seasons, the ca- 
lendars of the Jews and Mahometans, the eclipses of the Sun, 
Moon, and satellites of Jupiter ; the occultations of the fixed stars 
by the moon, the elements of the two comets of short period, 
known as Encke's and Biela's : the position and magnitude of the 
rings of Saturn, the aspects of the planets, the height of the 
greatest tides, the usual height of the spring tides at several 
places on the American coast, the difference between the time 
of high water at these places and at Boston, the latitude and lon- 
gitude of most of the principal places in the United States, and 
with the length of the longest and shortest days thereat, will, it 
is supposed, require no illustration. 

Of the calendar pages, those (36 and 37) for the month of 
January may be taken as an example. On the top of the left 
hand page will be found the apparent time of the beginning and 
end of twilight, or the time when the Sun is 18 degrees below 
the horizon before sunrise, and after sunset, for every sixth day, 
at Boston, New York, Washington, Charleston, and New Orleans ; 
which places being situated in different latitudes, renders the al- 
manac equally useful to every part of the United States. It may 
however be proper to remark, that the twilight will not in general 
be sufficiently strong to be visible, unless the Sun is considerably 
less than 18 degrees below the horizon. On the 1st of January 
it appears that the twilight begins at New Orleans at 27 minutes 
after 5 in the morning, and ends at 27 minutes before 7 in 
the evening. Under the above, will be found the time of the 
Moon's apogee and perigee, or the time in each lunation, when 



page II 



I'liitr 7 




Opposition 
liars 



THE EPHEMERIS. 45 

she is farthest from, and nearest to the Earth, with the dis- 
tance between the Earth and Moon, at those times, in English 
miles. 

Next below are placed the phases of the Moon, or the mean 
time at Washington of her conjunction, quadratures, and oppo- 
sitions with the Sun : under these are placed the columns of the 
calendar, viz. the day of the month and the corresponding day 
of the week, also the apparent time of the rising and setting of 
the Sun, and the mean time of the rising or setting of the Moon, 
calculated for the same cities for which the twilight was com- 
puted : thus, on the 2d of January the Sun rises at Boston at 
2 1 minutes after 7, and sets 3 1 minutes before 5 ; at New Orleans, 
he rises 57 minutes after 6, and sets 57 minutes before 6 ; the 
Moon sets the same day at Boston at 39 minutes after 4 in the 
afternoon, and at New Orleans 5 minutes after 5. By doubling 
the time of the Sun's rising we have the length of the night, and 
by doubling that of his setting, the length of the day ; hence, 
at Boston on the 2d of January, the length of the day, or the in- 
terval between the rising and setting of the centre of the Sun, 
exclusive of the effect of refraction, is 8 hours 58 minutes, and 
at New Orleans 10 hours 6 minutes : want of room is the reason 
assigned in the almanac for expressing the beginning and end of 
twilight and the rising and setting of the Sun in apparent time. 
Apparent time is, however, readily converted into mean, by apply- 
ing the equation (third long column right hand page) according 
to the direction at the head of the column ; and mean into ap- 
parent, by applying the equation contrary to the direction : thus, 
on the 2d of January the equation being 4 minutes to be added 
to apparent for mean time, and consequently to be subtracted from 
mean for apparent ; the Sun rose that day at Boston, in mean 
time, at 35 minutes after 7 and sat 27 minutes before 5 ; and the 
Moon sat the same day, in apparent time, at 30 minutes after 4. 

The column of the equation of time shows the quantity by 
which a well regulated clock is fast or slow of the Sun, and by 
it watches or clocks may be regulated, by comparing them with 
a good dial at any time when the Sun shines thereon, and ex- 



46 THE EPHEMERIS. 

amining if the difference between them agrees with the figures in 
this column: thus, on the first day of January 1832 ; a clock did 
not show true mean time unless it was 13 minutes 42 seconds 
faster than the time by the dial, or unless when the shadow in- 
dicated noon, the clock was 13 minutes 42 seconds past 12. — For 
further illustrations see the chapter on the equation of time, page 65. 

The second long column of the right hand page gives the 
mean time of the daily passage of the Moon over the meridian 
of Washington, or the instant her centre bears down South at 
that place. On the day of conjunction with the Sun, the Moon 
the planets, and the fixed stars come to the meridian very nearly 
at the same moment with him ; and if the conjunction takes 
place precisely at noon, the two bodies will be on the meridian 
precisely at the same time ; in all other positions than when in 
conjunction, the Moon, planets, and stars will pass the meridian 
before, or after the Sun, according as the Sun's right ascension 
is greater or less. The mean time of the passage of any hea- 
venly body over the meridian, is easily found by subtracting the 
siderial time at the moment of the passage, from the right ascen- 
sion of that body at the same moment 

The fourth, fifth, and sixth of the long columns contain the 
mean time of high water at Boston, New York, and Charleston, 
of that tide which arrives when the Moon is near to the meri- 
dian. The 7th long column contains the remarkable days in the 
month, the conjunction of the Moon with fixed stars and planets, 
that may be occultations in some part of the United States, and 
other phenomena interesting to the astronomer. At the top 
of the right hand page, will be found the mean time of the pass- 
age of the planets over the meridian of Washington, with their 
declinations or distance from the equator at that time, on every 
sixth day. By the assistance of this table, the places of the 
planets may be easily found in a celestial globe ; it being borne in 
mind, that north declinations are designated by the sign + and 
south by — . 

On pages 60, 61, 62, 63, are the Sun's declination, and the 
siderial time, which are given for every day, at noon, at Berlin ; 



THE EPHEMERIS. 47 

or about six in the morning at Washington, the former in appa- 
rent, the latter in mean time ; the greatest declination (23° 27^') 
will be found on the 21st of June and December: about the 
20th of March, and 23d of September, the declination ap- 
pears to be nothing ; the Sun's centre is, therefore, then but for 
a single moment in the celestial equator, which is vulgarly termed 
crossing the line ; the exact moment of the Sun having no 
declination, may be thus ascertained. On the 20th of March, 
1832, at apparent noon at Berlin, in Prussia, it appears by the 
almanac, the declination of the Sun's centre was 2' 59.2" south, 
and on the 21st 20' 41.3" north ; then by proportion as 23' 40.5" 
(the variation in 24 hours) is to 2' 59.2", so is 24 hours to 
3 hours 1 minute 40 seconds ; consequently the Sun's centre was 
in the celestial equator at Berlin, March 20th, 3 hours 1 minute 
40 seconds apparent, or 3 hours 9 minutes 14 seconds mean time 
in the afternoon : from which subtracting the difference of longi- 
tude, 6 hours 1 minute 41 seconds, (Washington being west of 
Berlin,) we have the corresponding time at Washington, March 
20th, 9 hours 7 minutes 33 seconds, mean time, in the morning. 
The Sun's siderial time, is what the Sun's right ascension 
would be, if the Earth moved uniformly in her orbit, and in the 
plane of the celestial equator; it therefore is the Sun's actual 
right ascension, diminished or increased by the equation of time* 
It is of the greatest importance for the determination of the mean 
time of the passage of the Moon, planets, or stars over the me- 
ridian, by subtracting it from the right ascension of the Moon, 
planet, or star, at the moment of the passage. If the latter be 
the greater, the passage will be after ; and if less, before that 
of the Sun. For example, the star Aldebaran will be on the 
meridian of Washington, August 28th, 1832, at 5 hours 59 mi- 
nutes 38 seconds mean time, in the morning, its right ascension 
at that moment being 4 hours 26 minutes 18 seconds ; and the 
siderial time 10 hours 26 minutes 40 seconds. 



48 POLES AND TROPICS, 



CHAPTER XVI. 

A Degree is the 360th part of a circle ; and the 
measure of an angle is an arc, or part of the circum- 
ference of a circle, whose angular point is the centre ; 
and so many 360th parts as an arc contains, so many 
degrees the measure of an angle is said to be : 

Thus, let A B (plate IX. fig. 3,) represent the plane of the ecliptic, 
and N C S the axis of the earth, Z C P will make an angle of 23£°, be- 
cause the arc, Z P, contains 23£ parts of 360, the whole circle ; and as 
A N contains the same number of degrees as Z P, its inclination must 
be 23P. 

The Poles are the extremities of the earth's axis, 
(plate IX, fig. 3 ;) N the north pole, S the south pole, 
P the north pole star, to which, and to the opposite part 
of the heavens, the axis always points. These extremi- 
ties in the heavens appear motionless, while all the 
other parts seem in a continual state of revolution. 
The circle of motion in the heavenly bodies seems to 
increase with the distance from the poles. 

The Tropics are two small circles parallel to the equa- 
tor, at 23 i degrees distance from it ; that to the north 
is called the tropic of Cancer, and that to the south the 
tropic of Capricorn. 

The Polar circles circumscribe the poles of the 
world, at the distance of 23^ degrees. That on the 
north is called the Arctic, and that on the south the 
Antarctic circle. 

The distance of these polar circles from the poles being fixed at 23£° 
(the same as the tropics from the equator) is because it is the line of 
boundary between light and darkness, when the sun is on either of the 
tropics, and throws his beams over and beyond the pole. 



pagt 49 



]'l„t, r, 



i 




MERIDIANS, COLURES, &C. 49 

The Meridians are so called because, as the earth 
revolves on his axis, when any one of them is opposite 
to the sun it is mid-day or neon along that line. Twen- 
ty-four of these lines are usually drawn on the globes, 
to correspond with the twenty-four hours of the day. 
Not that these are the only ones that can be imagined, 
for every place that lies ever so little east or west of 
another place has a different meridian. 

Suppose the upper 12 (plate IX. fig. 3.) to be opposite the sun, it 
will of course be noon along that line ; and the next meridian marked 1, 
being 15° east, will have passed the meridian 1 hour, consequently it 
will there be one in the afternoon, and so on, according to the order of 
the figures, to the lower 12, which being the part of the earth turned 
directly from the sun, it will be midnight on that meridian : as you pro- 
ceed round, the next meridian will be one in the morning, the next two, 
and so on, till you arrive at the upper 12, where you set off Hence 
there must be a continual succession of day and night. 

Note. This difference of time between places, lying under different 
meridians, is called longitude ; or, 

Longitude is an arc of the equator between the me- 
ridian of any place and the first meridian. In English 
geographers the first meridian passes through London 
or Greenwich, and the distance is reckoned east or 
west thence ; fifteen degrees of longitude being equal 
to one hour of time. 

To all places eastward of the first meridian, the time 
will be before London ; if west, after London. 

To reduce longitude to time divide by 15. 

As the earth makes a complete revolution on its axis in 24 hours, it 
must pass over 360° in that time : and if you divide 360 by 24, the quo- 
tient, 15, will be the number of degrees passed over in an hour : hence 
30° will be equal to two hours, 45° to three hours, &c. 

Then if it be 12 o'clock at London, at Barbadoes, lying nearly 60° 
west of London, it will be 4 hours earlier, or 8 o'clock in the morning. 
At Petersburgh, 30° east, it will be 2 hours later, or 2 o'clock in the 



50 LATITUDE, COLURES, &C. 

afternoon ; and at Calcutta, almost 90° east, nearly 6 hours later in the 
afternoon. 

To reduce time to longitude, multiply by 15. 

A captain arriving at the Bermudas, finds the difference of time be- 
tween them and London to be 4 hours and 20 minutes, which, multi- 
plied by 15 (or by 3 and 5) will give 65°. 

Latitude is the distance of any place from the equa- 
tor, either north or south, or it is equal to the elevation 
of the pole above the horizon. The latitude of the 
heavenly bodies is reckoned from the ecliptic, and ter- 
minates in the arctic and antarctic circles, and their 
longitude begins at the point Aries. 

The Colures are tico meridians, which pass through 
the poles of the world ; one of them through the points 
of Aries and Libra, and therefore called the Equinoc- 
tial Colure ; the other through the solstitial points, 
Cancer and Capricorn, and therefore called the Solsti- 
tial Colure. 

The Zones are five; namely, one torrid, two temperate, 
and two frigid. — The torrid is all that space between the 
tropics, and so called from its excessive heat ; the tem- 
perate zones extend from the tropics to the polar cir- 
cles ; the frigid zones are comprised between the polar 
circles and the poles. 

Solstitial points are the first points of Cancer and 
Capricorn ; so called because the sun, when he is near 
either of them, seems to stand still, or to be at the 
same height in the heavens at noon for several days 
together. 

Equinoctial points are the first points of Aries and 
Libra; so called, because when the sun is near either 
of them the days and nights are equal. 



planets' orbits elliptical. 51 

As it is presumed that the pupil will have previously gone through 
a course of geography and the globes, the above short definitions may 
be sufficient, though they could not be omitted altogether. 



CHAPTER XVII. 

PLANETS' ORBITS ELLIPTICAL, 

The orbits or paths described by the revolution of 
the planets round the sun, are not true circles, (as plate 
VIII. fig. 3,) but somewhat elliptical, that is, longer 
one way than another. 

In a circle the periphery, or circumference, is equal- 
ly distant from a point within, called its centre, A; but 
an ellipsis has two points called the focuses, or foci, as 
B C. In one of these, called its lower focus, is the sun. 
Hence, in every revolution of the planet it must be 
nearer the sun in one part of its orbit than it is at an- 
other. 

Let S (plate VIII. fig. 5,) represent the sun, A B C D 
a planet in different parts of its orbit ; when it is nearest 
the sun, as at A, it is said to be in its perihelion ; when 
at B its aphelion ; but when at C or D, its middle or 
mean distance; because the distance S C or S D is the 
middle between A S, the least, and B S the greatest ; 
and half the distance between the two focuses is called 
the eccentricity of its orbits, as S E or E F. 

ATTRACTION OF GRAVITATION. 

By attraction is meant that property in bodies by 
which they have a tendency to approach each other. 



52 ATTRACTION OF GRAVITATION. 

Thus the magnet attracts the needle ; this is called attraction of mag- 
netism : and thus the feather suspended near the electrical conductor, 
is attracted by it ; this is termed attraction of electricity. And that pro- 
perty which connects or firmly unites the different particles of matter, 
of which the body is composed (as that of a stone,) is attraction of coke- 

sion. 

• 

, Attraction of Gravitation is a power by which bo- 
dies in general tend toward each other ; and the at- 
traction is in proportion to the quantity of matter which 
they contain ; but the earth, being so immensely large 
in comparison of all other substances in its vicinity, de- 
stroys the effect of this attaction between smaller bo- 
dies by bringing them all to itself. 

By attraction of gravitation, the sun, the largest body, 
attracts the earth and all the other planets, and they 
again gravitate or have a tendency to approach the sun. 
The earth being larger than the moon, attracts her, and 
she gravitates towards the earth. 

Upon this principle, a stone, when thrown from earth, is brought 
by the earth's attraction and its own gravitating power to the earth 
again. 

The waters in the ocean, and indeed all the terrestrial bodies, gra- 
vitate towards the centre of the earth ; and it is by this power that we 
stand on all parts of the earth, with our feet pointing to the centre. In 
short, it is by the attraction of gravity that a marble falls from the hand, 
a brick from the top of a building, or an apple from the tree. All bo- 
dies, by the power of gravity, have a tendency or disposition towards 
the earth. 

One law of attraction is, " That attraction decreases 
as the squares of the distances from that centre in- 
crease" 

Any number multiplied into itself is a square number ; thus, the 
square of 2 is 4, the square of 3 is 9, of 4 is 16, &c. 

Suppose a planet at B (plate X. fig. 4,) to be twice 



ATTRACTION OF GRAVITATION. 53 

as far from the sun as at A ; then, as the square of the 
distance 2 is 4, the attraction at B will be four times 
less than at A, or, which is the same thing, A will be 
attracted with four times the force it would be at B. 

Again, if the distance at A (fig. 5,) were four times 
less than at B, then, as the square of 4 is 16, the at- 
traction at A would be sixteen times greater than at B. 

The second law of gravity is, " That bodies attract 
one another with forces proportional to the quantities 
of matter they contain" All bodies of equal magnitude 
contain not equal quantities of matter, for a ball of cork 
of equal bulk with one of lead, being more porous, does 
not contain so much matter. 

So the sun, though a million of times as big as the 
earth, not being so compact and dense a body, contains 
a quantity of matter only 200,000 times as great, and 
hence attracts the earth with a force only 200,000 
times more than the earth attracts him. 

Hence suppose there are in a river two boats of 
equal bulk at any distance, suppose twenty yards, from 
each other, and that a man in one boat pulls a rope 
which is fastened to the other, the boats will meet in 
a point which is half way between them. If one boat 
were three times the bulk of the other, then the lighter 
would move three times as far as the heavier, ox fifteen 
yards, while the heavier moved only^e. 



54 ATTRACTIVE AND PROJECTILE FORCES. 



CHAPTER XVIII. 

OF ATTRACTIVE AND PROJECTILE FORCES. 

The sun, being so immense a body, would, by the 
power of attraction draw all the planets to him, if the 
attractive power were not counteracted by another force. 
It must therefore be observed that all simple motion is 
naturally rectilineal, that is, all bodies, if there were 
nothing to prevent them, would move in straight lines. 
But the planets' motions are circular, which is a com- 
pound of two forces, the one called the attractive or 
centripetal force; the other the projectile or centrifugal 
force. 

Suppose a marble be shot from the hand along a smooth floor, if it 
meet with no impediment it will move straightforward ; this is termed 
the projectile force, and its motion will be rectilineal. But if a ball be 
thrown into the air, unless projected perpendicularly, it will not con- 
tinue to move in a straight line, but incline towards and fall to the 
earth ; for the resistance of the air, and the attraction of the earth retard 
its progress : otherwise it would continue to move in a straight line, 
with a velocity equal to that which was at first impressed upon it. 

The joint action of the attractive or projectile forces 
retains the planets in their orbits ; the primaries round 
the sun, and the secondaries round their primaries. 

When a stone is whirled round in a sling, its motion is circular. If 
the stone flies out, it will go off in a straight line. 

This straight line is what is called the tangent of a circle, as A a, B 
b, &c. (Plate VIIL fig. 4;) for all bodies moving in a circle have a 
natural tendency to fly off in that direction. Thus a body at A will 
tend towards a, at B towards b, and so on, its rectilineal motion ; but 
the central force (the action of the hand) acting against it, preserves 
its circular motion. 

The moon and all the planets move by this law ; and 



ATTRACTIVE AND PROJECTILE FORCES. 55 

the attractive or centripetal force of the sun being 
equal to the projectile or centrifugal force of the plan- 
ets, they are, by attraction, prevented from moving on in 
a straight line, and, as it were, drawn towards the sun ; 
and by the projectile force from being overcome by at- 
traction. They must therefore revolve in nearly circu- 
lar orbits. 

If, for instance, the projectile force were to cease acting upon the 
earth, it must fall to the sun : on the contrary, if the force of gravity 
were to cease upon the earth, it would fly off into infinite space. 

The secondary planets are governed by the same 
laws in revolving round their respective primaries ; for 
as by the attractive power of the sun, combined with 
the projectile force of the primary planets, they are 
retained in their orbits; so also the action of the pri- 
maries upon their respective secondaries, together with 
their projectile force, preserves them in their orbits. 

If the attractive power of the sun were uniformly the 
same in every part of their orbits, they would be true 
circles, and the planets would pass over equal portions 
in equal times ; but the attractive power of the sun is 
not uniformly the same ; hence the orbits of the planets 
are not true circles, but a little elliptical, and they 
must pass over unequal parts of their orbits in equal 
portions of time. 

By passing over equal portions in equal times may be understood pas- 
sing from B to C, or from C to A, in the same time as from A to D, or 
from D to B.— (Plate VIII. fig. 5.) 

By unequal portions in equal times, the centrifugal force would carry 
a planet from A to a, in the same time as it would from B to b. And 
in its orbit from A to c, as soon as from B to d. 

A double velocity will balance a quadruple or fourfold 
power of gravity or attraction. — Hence, as the centri 



56 ATTRACTIVE AND PROJECTILE FORCES, 

petal force is four times as great at A as at B, the cen- 
trifugal force is twice as great ; and would describe the 
area or space contained between the letters A S c, in 
the same time as the area or space B S d. For accord- 
ing to the laws of the planetary motions, in their re- 
volutions they always describe equal areas in equal 
times. 

By equal areas is meant, that if the earth moves from A to c in the 
same time as from B to d, then the area of A S c will be equal to the 
area of B S d. 

The orbits of the comets being very elliptical, the 
irregularity of their motions must be exceedingly great. 

When near the sun, or in their perihelion, the cen- 
tripetal force must act powerfully on the comet, and 
that force must be equalled by the projectile force ; 
hence they will then move with amazing celerity ; but 
when arrived at their aphelion, where the influence of 
the sun is weak, their motion is exceedingly slow, and 
the sun must appear little more than a fixed star. 

If a body at rest receives two impulses at the same time, from forces in 
different directions, it will be made to move in a line that lies between 
the direction of the forces impressed. If on the ball A (Plate IX. fig. 
1,) a force be impressed sufficient to make it move with a uniform ve- 
locity to the point B, in a second of time ; and if another force be also 
impressed on the ball which would make it move to C, in the same 
time, the ball by means of the two forces acting together, will describe 
the line A a D. 

In the beginning the Grand Mover impressed such a degree of mo- 
tion upon these bodies as, if not controlled, would have whirled them 
onwards in straight lines to endless lengths, till they would have been 
lost to imagination in the abyss of space ; but the gravitating power 
combined with the projectile, determines their courses to an elliptical 
form, and obliges these bodies to perform their destined rounds. 



paqc M 



Flat, 9 




ON THE CENTRE OF GRAVITY. 57 

CHAPTER XIX. 

ON THE CENTRE OF GRAVITY. 

The Centre of Gravity is that point of the body, in 

which its whole weight is, as it were, concentrated, and 

upon which, if the body be freely suspended, it will 

rest. 

A weight of 1 cwt. at 10 feet from a prop, will balance another of 
10 cwL at 1 foot from it ; or 

Let two weights (Plate X. fig. 6) be nicely poised on 
a centre, round which they may freely turn : the 
heaviest, of 10 cwt., would move in a circle whose ra- 
dius or distance from the centre would be one foot, 
while the lightest, of 1 cwt., would move in a circle 
whose radius would be 10 feet ; the centre round which 
they move is the centre of gravity. 

And thus the sun and planets move round an ima- 
ginary point as a centre, always preserving an equilib- 
rium. 

If the earth were the only attendant on the sun, as his quantity of 
matter is 200,000 times as great as that of the earth, he would revolve 
in a circle a 200,000th part of the earth's distance from him, in the 
same time as the earth is making one revolution in its orbit, or one 
year ; but as the planets in their orbits must vary in their positions, 
the centre of gravity cannot be always at the same distance from the 
sun. 

The quantity of matter in the sun so far exceeds that 
of all the planets together, that even if they were all 
on one side of him, he would never be more than his 
own diameter distant from his centre of gravity ; there- 
fore the sun is considered as the centre of the system. 

As the secondary planets are governed by the same 
f 2 



58 THE HORIZON. 

laws as their primaries, they, also, with their primaries, 
move round a centre of gravity. 

Every system in the universe is supposed to revolve 
in like manner, and all these together to move round 
one common centre. 

THE HORIZON. 

The Horizon is that distant boundary of our sight 
where the heavens and the earth seem to meet all 
around us. 

There are two horizons, termed the rational and the 
sensible. The rational horizon applies to the rising, 
setting, &c. of the sun, moon and stars. This horizon 
is supposed to encompass the globe exactly in the mid- 
dle, or to be in a line with its centre H O, and to di- 
vide the heavens into two equal parts, being 90° distant 
from a point Z, over our heads, called the zenith; 
and the opposite point N, in the heavens directly under 
our feet called the nadir. (See Plate IV. fig. 2.) 

The rational horizon is represented on the artificial globes by the 
broad paper circle or wooden horizon. 

The sensible horizon respects land and water, and 
terrestrial objects. The extent of this horizon is great- 
er or less, according as the spectator is more or less 
elevated. 

Let oBc, (Plate IV. fig. 2,) represent the sensible horizon, and B the 
place of the spectator. Then an eye placed at 5 feet above the sur- 
face of the sea, sees 2 J miles each way ; but if it be elevated twenty 
feet, that is four times the height, it will see 5£ miles, or twice the 
distance. 

The difference of the two horizons is this : the sensible is seen from 
the surface of the earth ; the rational is supposed to be viewed from 
its centre. 



I 

DAY AXD NIGHT. 59 

Though the heavenly bodies can be viewed by the 
spectator only from the sensible horizon (or surface of 
the earth) as at B, yet they are really seen to rise and 
set when they are on the rational horizon, HO. This 
is owing to their vast distances from the earth, which 
occasion the difference arising from the positions of 
the surface or the centre to vanish. 

The semi-diameter of ihe earth is not 4,000 miles ; but 4,000 miles, 
compared with 95,000,000, the distance of the sun from the earth, is so 
little, that the difference of time is not discernible, not to mention the 
greater distance of the fixed stars. Even the rising and setting of the 
moon respects the rational horizon, whose distance is but 240,000 miles, 
which bears a proportion to 4,000, as 60 to 1. 



CHAPTER XX. 

DAY AND NIGHT. 

The form of the earth, as has been already noticed, 
approaches nearly to that of a true globe or sphere ; 
and the cause of the succession of day and night, is 
the rotation of the earth vpon its axis once in twenty- 
four hours. 

For the meaning of globe, or sphere, axis, &c. see Preliminary Defini- 
tions, chap. 1. 

A common observer may imagine that the sun, moon, and starry fir- 
mament revolve daily about the earth, while the earth remains at rest ; 
but their apparent motions are accounted for much more rationally. 

Suppose ABCD (plate IV. fig. 2) to be the earth 
revolving on its axis according to the order of the let- 
ters, that is, from A to B, from B to C, &c. If the sun 
be fixed in the heavens at Z, and a line, H O, be drawn 
through the centre of the earth E, it will represent the 



60 DAY AND NIGHT. 

circle, which, when extended to the heavens, is called 
the rational horizon. 

The sun always illuminates one hemisphere of the 
earth, while the other hemisphere remains in darkness. 

Therefore if the sun be supposed at Z, it will illu- 
minate by its rays all that part of the earth that is above 
the horizon H O. To the inhabitants at A, its western 
boundary, it will appear just rising ; to those situated 
at B, it will be noon ; and to those in the eastern part 
of the horizon C, it will be setting. 

A spectator cannot from any spot behold more than 
a semicircle of the heavens at any one time. If placed 
at A, he will see the concave hemisphere Z O N ; and 
on the boundary of his view will be N and Z ; conse- 
quently the sun at Z will be just coming into sight, or 
rising. 

Then by the rotation of the earth, he will in a few 
hours come to B, when to him it will be noon ; and 
those who live at B will have descended to C. 

In this situation they will behold the hemisphere 
N H Z, and the sun, Z, will to them be setting ; con- 
sequently it will be night to them till they return to A, 
when the sun will again appear to rise. 

Therefore, however a spectator may imagine that the sun and 
heavenly bodies are moving around him from east to west, this is only 
apparent ; just as a person passing swiftly in a carriage, or sailing 
near the shore, sees the houses, trees, and other fixed objects moving 
the contrary way ; but he knows that this is merely a deception, and 
that it is himself only that moves. 

This daily motion of the earth round its axis accounts 
equally for the apparent motions of the whole starry 
firmament about the earth every twenty-four hours. 



ON THE ATMOSPHERE. 61 

By this moiion the inhabitants of London arc carried at the rate of 
810 miles an hour, and those upon the equator about 1040. 

The only points in the heavens that keep their posi- 
tions, are the two celestial poles, which are opposite to 
the poles of the earth. 

The stars above our horizon are as numerous by day 
as by night; but they cannot be discerned, because 
the sun's rays are so powerful as to render those coming 
from the fixed stars invisible. 

Though our year consists of 365 days, the earth 
makes 366 revolutions on its axis, whilst it is going 
once round the sun. 

Though the earth makes a complete revolution daily 
on its axis, yet we are not at all sensible of its motion. 
If its motion were irregular, it would no doubt be per- 
ceptible ; but as it meets with no obstruction, the 
motion must be so uniform as not to be perceived. 

That the earth may have such a motion, and we not be in the least 
sensible of it, is evident ; for even the motion of a ship on smooth water 
is not sensibly perceived by those on board. 



CHAPTER XXI. 

OF THE ATMOSPHERE. 

The Atmosphere is a thin, transparent, and fluid 
body, surrounding this terraqueous globe, and covering 
it to a considerable height. It possesses permanent 
elasticity and gravity, and is most dense or heavy near 
the earth, but becomes gradually rarer or lighter, the 
higher we ascend ; so much so that at the tops of some 
high mountains it is difficult to breathe. 



62 OF THE ATMOSPHERE. 

The whole mass of the atmosphere contains a heterogeneous col- 
lection of particles, exhaled from all solid or fluid bodies on the surface 
of the earth. 

It serves not only to suspend the clouds, furnish us 
with wind and rain, and answer the common purposes 
of breathing, but is also the cause of the morning and 
evening twilight, and of all the glory and brightness of 
the firmament. 

Experiments upon the air-pump prove, that without the air or atmo- 
sphere no animal could exist; without its aid all vegetation would 
cease. Sound could not be produced without it, nor would there be 
any rains or dews to moisten the ground. 

Without an atmosphere, only that part of the sky 
would appear light in which the sun was placed ; and 
if a person should turn his back, the heavens would 
appear dark as night, and the least stars would be seen 
to shine. But the atmosphere being strongly illuminated 
by the sun, reflects the light back upon us, and causes 
the whole heavens to shine with such splendour as to 
render the light of the stars invisible.- 

The height to which the atmosphere extends has not 
been exactly ascertained ; but at a greater height than 
45 miles it will not refract the rays of light from the sun. 

The sun's rays falling upon the higher parts of it be- 
fore rising, causes by reflection a faint light, which in- 
creases till he appears above the horizon ; and in the 
evening decreases after he sets, till he is eighteen de- 
grees below the horizon, where the morning twilight 
begins, and the evening twilight ends. 

The beginning and end of twilight is also said to be when the least 
stars, viz. those of the 6th magnitude begin to appear and disappear. 



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I 



REFRACTION. 63 

CHAPTER XXIL 

REFRACTION. 

The rays of light, in passing out of one medium into 
another of a different density, deviate from a rectilineal 
course ; and if the density of this latter medium con- 
tinually increase, the rays of light, in passing through 
it, will deviate more and more from a right line towards 
a curve, in passing to the eye of an observer. 

From this cause all the heavenly bodies, but the moon, 
except when in the zenith, appear higher than they 
really are. This apparent elevation of the heavenly 
bodies above their true altitude, is caused by Refrac- 
tion. 

Let ABC (plate XI. fig. 1.) represent the surrounding atmosphere, 
a the true place of a star, b the apparent place. Let a ray fall from a 
on the surface of the atmosphere at A, and it will be refracted in the 
direction of the curve A D, because the density of the atmosphere in- 
creases as it approaches the earth's surface. Hence an observer at D 
will see the object at b. 

It is in consequence of the refraction of the atmo- 
sphere, that all heavenly bodies, except the moon, are 
seen for a short time before they rise in the horizon, 
and also after they have sunk below it. 

At some periods of the year the sun appears three 
minutes longer, morning and evening, than he would 
do were there no refraction ; and about two minutes every 
day at a mean rate. Hence, when the sun is at T below 
the horizon, a ray of light T I, proceeding from him, 
comes straight to I, where falling on the atmosphere, 
it is turned out of its direct, or rectilineal course, and 
is so bent down to the eye of the observer at D, that 



64 PARALLAX. 

the sun appears in the direction of the refracted ray 
above the horizon at S. 

The effects of refraction may be seen thus : immerse a staff in a tub 
of water ; if it be placed perpendicularly there will be no refraction ; 
that is, it will not seem bent at all : — incline it a little towards the edge 
of the tub, and it will appear a little bent at the surface of the water; 
incline it still more, and the refraction will be greater. 

Refraction is also shown in that well known experiment of putting 
any small object, as a shilling, &c, at the bottom of a basin or tub, then 
walking backward till the object is just lost sight of, and there stand- 
ing while another person pours water into the basin, and the money 
will appear Now if the edge of the basin be called the horizon, the 
water the atmosphere, and the shilling the moon, it is clear that it will 
be seen above the horizon when really below it. 



CHAPTER XXIII. 

PARALLAX. 

The Parallax of the sun and moon is the difference 

between the altitude of either object observed at the 

same instant of time by two spectators ; one on the sur» 

face of the earth, and the other placed at the earth's 

centre. 

The place of an object as observed from the earth's surface is called 
its apparent place ; and as observed from the centre, its true place. 

The parallax of the heavenly bodies is greatest when 
in the horizon; hence called the horizontal parallax. 

The sun's mean parallax being only 8.6, is seldom made use of in 
nautical calculations, except to determine the longitude, by means of 
observing the angular distance between the sun and moon. 

The fixed stars, on account of their vast distance from the earth, 
have no parallax. 

As the parallax of the sun or moon or planets de- 
presses, or causes them to appear lower than they really 



EQUATION OF TIME. 65 

are, the difference must be added to their apparent al- 
titudes, to obtain their true altitudes. 

Let C (fig. 2, plate XI.) represent the centre of the 
earth ; F D E, part of the moon's orbit ; G d e, part of 
a planet's orbit ; Z K, part of the starry heavens : now, 
to a spectator at A, upon the surface of the earth, let 
the moon appear at E, in the horizon of A, and it will 
be referred to K ; but if viewed from the centre C, it 
will be referred to I: the difference between these 
places, or the arc I K, is called the parallax in alti- 
tude; and the angle A E C, is the parallactic angle. 

The parallax will be greater or less, as the objects 
are more or less distant from the earth ; thus the paral- 
lax I K, of E, is greater than the parallax/ K, of e. 

Also, with respect to any one object, when it is in 
the horizon, the parallax is the greatest, and diminishes 
as the body rises to the zenith, where the parallax is 
nothing. Thus, the horizontal parallax of E and e, is 
greater than that of D and d; but the objects F and G, 
as seen from either A or C, appear in the same place 
Z, or in the zenith. 



CHAPTER XXIV. 

EQUATION OF TIME. 

Our summer half year is longer than the winter 
half year, by about eight days ; occasioned by the 
inequality of the earth's annual motion. This in- 
equality and the obliquity of the ecliptic are the 
causes of the difference of time between the sun and 
a well regulated clock. The clock keeps equal time, 

G 



66 EQUATION OF TIME. 

while the sun is constantly varying, and shows only ap* 
parent time. The difference of these is called the 
equation of time. 

Equal time is measured by a clock that is supposed to measure ex- 
actly 24 hours from noon to noon. And apparent time is measured by 
the apparent motion of the sun in the heavens, or by a good sun-dial. 

This difference between equal and apparent time de- 
pends, first, upon the inclination of the earth's axis to 
the plane of its orbit ; and secondly, upon the elliptic 
or oval form of the earth's orbit; for the earth's orbit 
being an ellipse, its motion (as has been already shown) 
is quicker in its perihelion than in its aphelion. 

The rotation of the earth upon its axis is the most 
equable motion in nature, and is completed in 23 hours, 
56 minutes, and 4 seconds. This space is called a 
sidereal day, because any meridian on the earth will 
revolve from a fixed star to that star again in this time. 

Hence, if the earth had only a diurnal motion, the day would be 
nearly four minutes shorter than it is. 

But a solar, or natural day, which our clocks are in- 
tended to measure, is the time which any meridian on 
the earth will take in revolving/ro?tt the sun to the sun 
again, which is about 24 hours, sometimes a little more, 
sometimes less. This is occasioned by the earth's ad- 
vancing nearly a degree in its orbit, in the same time 
that it turns eastward on its axis ; and hence the earth 
must make more than a complete rotation before it can 
come into the same position with the sun, that it had 
the day before. 

Some idea of this may be formed by the hands of a clock ; suppose 
both of them to set off together at twelve o'clock, the minute hand 



EQUATION OF TIME. 67 

must travel more than a whole circle before it will overtake the hour 
hand ; that is, before they will be in the same relative position. 

Again, it must be observed that only four times a year 
the degrees on the ecliptic and the equation are equal ; in 
other words, but four times a year is the sun's longitude 
and right ascension the same in degrees ; and that is 
when he passes through the equator and the tropics, 
and then the" sun and clocks go together, as far as re- 
gards this cause; but at other times they differ, because 
equal portions at the ecliptic pass over the meridian in 
unequal parts of time, on account of its obliquity. 

To those who are acquainted with the globes this will appear evi- 
dent by inspection. First, find the sun's longitude on the eclip- 
tic, then his right ascension on the equator, and it will be seen that 
the number of degrees will be nowhere equal, except at the first point 
of Aries, Cancer, Libra and Capricorn. Or, it may be illustrated by the 
globe, thus : (plate IX. fig. 2 :) Let op and =£= represent the equator : 
op, 25, :£= the northern half of the ecliptic, and Op, ]£?, =£s the southern 
half. Make chalk or other marks, as&tabcdefgh, all round the 
equator and ecliptic at equal distances (suppose at 20 or 30 degrees from 
each other,) beginning at Aries ; now, by turning the globe on its axis, 
it will be seen that all the marks in the ecliptic, from Aries to Cancer, 
come sooner to the brazen meridian than their corresponding marks on 
the equator : those from the 1st of Cancer to Libra, come later ; — those 
from Libra to Capricorn sooner, and those from Capricorn to Aries later. 

Note : Time, as measured by the sun-dial is represented by the 
marks on the ecliptic ; that measured by a good clock, by those on the 
equator. 

Hence it may be supposed, that while the sun is in 
the first and third quarters (plate IX. fig. 2,) that is, 
between °P and 25, and =£= and V5, it will be faster than 
the clocks, and while in the other two quarters it will 
be shiver; because equal portions of the ecliptic come 
sooner to the meridian in the 1st and 3d, and later in 
the 2d and 4th ; but on account of the elliptic form of 



68 EQUATION OF TIME. 

the earth's orbit, this will not be always exactly the 
case. 

If the difference between time measured by the dial and clock, de- 
pend solely on the inclination of the earth's axis to the plane of its orbit, 
the clocks and dials ought to be together both at the equinoxes and the 
solstices (that is, on the 20th March, 21st June, 23d September, and 21st 
December ;) but owing to the elliptic form of the earth's orbit, they co- 
incide on other days not far distant. 

An Ephemeris will show this : on the 20th March, and 23d of Sep- 
tember, instead of the clocks and dials agreeing, there will be a varia- 
tion of 6 or 8 minutes : and their times of coinciding will happen seve- 
ral days later in the vernal, and earlier in the autumnal equinox. 

If the earth's motion in its orbit were uniform, which 
it would be if the orbit were circular, then the whole 
difference between equal time by the clock, and appa- 
rent time by the sun, would arise from the inclination 
of the earth's axis. But this is not the case ; for the 
earth travels when nearest the sun, that is in the winter, 
more than a degree in 24 hours ; — and when farthest 
from the sun, that is in summer, less than a degree in 
the same time. 

From this cause the natural day would be of the 
greatest length when the earth was nearest the sun, for 
it must continue turning the longest time after an en- 
tire rotation, in order to bring the meridian of any place 
to the sun again ; and the shortest day would be when 
the earth moves the slowest in her orbit. 

The above inequalities, combined with those arising 
from the inclination of the earth's axis, make up that 
difference which is shown by the equation table in one 
of the outside columns of an Ephemeris. 



THE SEASONS. 69 

CHAPTER XXV. 

THE SEASONS. 

The axis of the earth is not upright or perpen- 
dicular to the plane of the ecliptic, but inclines to 
it 23J degrees, as Z C P, making an angle with it of 
661 degrees, PCB, (plate IX. fig. 3.) The axis of 
the earth, in its annual orbit, always keeps parallel to 
itself. 

See plate XII. fig. 2, where the earth is represented in four different 
parts of its orbit, still preserving its parallelism ; see also plate XIII. 
fig. 1. 

Although the earth's orbit is 190,000,000 of miles in 
diameter, yet the axis of the earth always points to the 
same part of the heavens ; because compared with the 
distance of the fixed stars, 190,000,000 of miles is but 
a mere point 

As some illustration of this : suppose two parallel lines are drawn 
upon an elevation, three or four yards from each other. If we look 
along them they will both seem to point directly to the moon in the ho- 
rizon, and perhaps three or four yards will bear as great a proportion 
to the moon's distance, as 190,000,000 of miles to the fixed stars. 

What a striking proof of the inconceivable distance of the fixed stars, 
when, notwithstanding the earth in the course of the year continues 
to move from one part of its orbit to the other, yet the north pole ap- 
pears at all times to point in exactly the same direction towards the po- 
lar star ! 

It is known that the earth has an annual course round 
the sun, because the sun, if seen to be in a line with a 
fixed star, any day or hour, will in a few weeks, by the 
motion of the earth, be found considerably to the east 
of such star, and he may be thus traced round the hea- 
vens to the same fixed star from which he set out. 

g 2 



70 THE SEASONS. 

These observations may be made in the day-time, because through 
the shaft of a very deep mine the stars are visible by day as well as by 
night. They are also rendered visible in the day by telescopes pro- 
perly fitted up for the purpose. 

The variety of the seasons depends upon the length 
of the days and nights, and upon the position of the 
earth with respect to the sun. 

If the axis of the earth N S (plate X. fig. 1) were 
perpendicular to a line E Q, drawn through the cen- 
tres of the sun and earth, there would happen equal 
day and night throughout the year ; for as the sun al- 
ways enlightens one half, every part must be half its 
time in the light, and the other half in darkness. 

The two poles must be excepted, because to a person there situated, 
the sun would never appear to rise or set, but would always be mov- 
ing round the horizon. 

If the earth were thus situated, the rays would fall at 
all times vertically on the equator : and the heat excit- 
ed by the sun being greater or less, in proportion as the 
rays fall more or less perpendicularly, the parts about 
the equator would be heated to a high degree, while 
the regions around the poles would be desolated by 
perpetual winter. 

The proportion of heat materially depends on the degree of perpen- 
dicularity of the sun's rays. Let plate X. fig. 3, represent summer and 
winter rays in the latitude of London. It is evident that the summer 
rays strike more directly, and with greater force, as well as in greater 
numbers, on the same place. 

The axis of the earth being inclined 23|° as in plate 
X. fig. 2, represents the position of the earth in our 
summer season, when all the parallel circles, except 
the equator, are divided into two unequal parts; and 
the length of their days and nights in each latitude will 



TIIE SEASONS. 71 

bear a proportion to the greater or less portion of their 
circumference in the enlightened and dark hemisphere. 

If, for instance, a b represent that circle of latitude in which London 
is situated, it is evident that about two-thirds of it is in the light, and 
only one-third in darkness ; hence, the sun will be two-thirds or 16 
hours above the horizon, and 8 hours below it. 

The parallel above a b is entirely in the light, and from thence to 
the pole there is continual day for some time ; and at the pole the sun 
shines for six months together. 

During that time the south pole is involved in darkness. 

To those who live in equal latitudes, the one north, 
the other south, the length of the days to one will be 
always equal to the length of the nights to the other. 

All parts of the globe enjoy the presence of the sun 
for the same length of time, in the course of the. year. 



CHAPTER XXVI. 

THE SEASONS, CONTINUED. 

The figure plate XII. fig. 2, represents the earth 
in four different parts of its orbit, or as situated with 
respect to the sun in the months of March, June, Sep- 
tember, and December. The earth appearing nearer 
the sun in winter than in summer. 

We are more than 3,000,000 of miles nearer to the sun in December 
than we are in June ; and as the apparent diameter of any object in- 
creases in proportion as our distance from it is diminished, so the sun's 
apparent diameter is greater in our winter than in summer. In winter 
it is 32' 36", in summer but 31' 31". 

It is ascertained that our summer (that is, the time 
that passes between the vernal and autumnal equinoxes) 
is nearly eight daye longer than our winter, or the time 



72 THE SEASONS. 

between the autumnal and vernal equinoxes ; conse- 
quently the motion of the earth is slower in summer 
than in winter, and therefore it must be a greater dis- 
tance from the sun. 

The coldness of our northern winters (though nearer to the sun,) 
compared with our summers, arises from the rays falling upon us so 
very obliquely, as was before noticed ; and also from the length of the 
summer days and shortness of the nights ; for the earth and air become 
heated by day, more than they can cool by night. 

Both the hottest and coldest seasons of the year are not in the long- 
est and shortest days, but a month after those times ; for a body once 
heated does not grow cold instantaneously, but gradually, and vice 
versa. And as long as more heat comes from the sun in the day than 
is lost in the night, the heat will increase. 

In June the north pole of the earth inclines to the 
sun (plate XII. %. 2,) and consequently brings all the 
northern parts of the globe into the light ; then to the 
people of those parts it is summer. But in December, 
when the earth is in the opposite part of its orbit, the 
north pole declines from the sun, and the south pole 
comes into light. It is then winter to us, and summer 
to the inhabitants of the southern hemisphere. 

In March and September the axis of the earth neither 
inclines to, nor declines from the sun (plate XII. fig. 
2,) but is perpendicular to a line drawn from its cen- 
tre. 

It is then equal day and equal night at all places, 

except at the poles, which are in the boundary of light 

and darkness, and the sun being directly vertical to, 

or over the equator, makes equal day and night at all 

places. 

In March the real place of the earth is Libra, consequently the sun 

will appear in the opposite sign, in Aries, and be vertical to the equator 

As the earth proceeds from March to June, its northern hemisphere 



THE MOOD'S MONTHS, PHASES, ETC. 73 

romes into light, and on the 21st of that month, the sun is vertical to 
the tropic of Cancer. 

In September the sun is again vertical to the equator, and of course 
the days and nights are again equal. 

Following the earth in its journey to December, or when it has ar- 
rived at Cancer, the sun appears in Capricorn, and is vertical to the 
tropic of Capricorn. Now the southern pole is enlightened, and all the 
circles on that hemisphere have their larger parts in light. Of course 
it is summer to the southern, and winter to the northern hemisphere. 

For the increase and decrease of days and nights 
we are indebted to the inclination of the earth's axis, 
and its preserving its parallelism. Hence from the 
20th of March to the 21st of June the sun is vertical 
successively to all places between the equator and the 
tropic of Cancer, and consequently the days must grad- 
ually lengthen. From June to September the sun is 
again successively vertical to the same parts of the 
earth, but in a reverse order. 

From September to December the sun is sucessively vertical to all 
places between the equator and the tropic of Capricorn, which causes 
the days to lengthen in the southern hemisphere. 



CHAPTER XXVII. 

THE MOON'S MONTHS, PHASES, ETC. 

The time which the moon takes in performing her 
journey round the earth, is called a month, of which 
there are two kinds; a periodical month of 27 days, 7 
hours, 43 minutes, and a synodical month of 29 days, 
12 hours, 44 minutes, nearly. 

This difference arises from the earth's annual motion 
in its orbit. 



74 PHASES OF THE JIOON. 

Suppose (plate XII. fig. 1.) S the sun ; T the earth, in a part of its 
orbit QTL. Let E be the position of the moon. If the earth had no 
motion, the moon would move round its orbit, E F G, &c. into the po- 
sition of E again in 27 days, 7 hours, 43 minutes ; but while the moon 
is describing her journey, the earth is passing through nearly a twelfth 
part of its orbit This the moon must also describe, before the two 
bodies can come again into the same position that they before held 
with respect to the sun ; and this takes up so much more time as to 
make her synodical month equal to 29 days, 12 hours, and 44 minutes. 
This is the cause of the division of time into months. 

N. B. The moon's orbit is elliptical. 



THE PHASES OF THE MOON. 

The sun always enlightens one half of the moon ; 
and though sometimes its whole enlightened hemis- 
phere is seen by us, yet sometimes only a part, and at 
other times none at all, is discernible, according to her 
different positions in the orbit, with respect to the 
earth. 

Suppose (plate XII. fig. 1,) A B C D E, &c. to represent the moon 
in different parts of her orbit round the earth, in which one half is cou- 
stantly seen to be enlightened, as would appear if seen from the sun ; 
then will the enlightened parts of the outside figures represent the ap- 
pearance of the moon as seen from the earth. 

When the moon is at E, no part of its enlightened 
side is visible to the earth. It is then new moon or 
change. And the moon being in a line between the 
sun and the earth, they are said to be in conjunction. 

The outside figure opposite E is wholly dark, to show that the moon 
is invisible at cliange. 

The whole illuminated hemisphere at A is turned to 

the earth, and this is called full moon, and the earth 

being between the sun and moon, they are said to be in 

opposition. 



ptu/t' 75 



Tlatell 



** 



(l #. 



REFRA CTI02? 



Fuj. 1 







T * 4. * 



•h- 



/}>. 2 






// /% 




FAR IFF AX 



ECLIPSES. i O 

When at F, a small part only will be seen from the 
earth, and that will appear horned ; at G, one-half of 
the enlightened hemisphere is visible ; it is then said 
to be in quadrature. 

At H, three-fourths of the enlightened part are visi- 
ble, and it is then said to be gibbous; and at A, the 
whole enlightened face is said to be full, and so of the 
rest. 

The horns of the moon just after change, or conjunction, are turned 
to the east ; aherfull moon, or opposition, they are turned to the west 

The various phases of the moon are often represented by a small 
globe or ivory ball suspended by a string. Let your eye represent the 
earth, and the candle the sun ; then moving it round you, the full and 
the change will appear, and the different degrees of illumination in her 
orbit as seen from the earth. This will also illustrate the manner in 
which the moon, by keeping the same face always towards the earth, 
makes one complete revolution on her axis while she makes one in her 
orbit. 

The moon's apparent motion is that of rising in the 
east and setting in the west, but this is owing to the 
revolution of the earth upon its axis. The moon's real 
motion round the earth is from west by south to east. 

Her real motion may be known by remarking, when she is near any 
particular star, she will approach it from west to east, then be in con- 
junction with it, and then pass eastward of it. 



CHAPTER XXVIII. 



ECLIPSES. 



The term Eclipse implies a privation of light, and 
in Astronomy the obscuration of the luminaries of 
heaven. Eclipses are either of the sun or moon. 



76 ECLIPSE OF THE MOON. 



ECLIPSE OF THE MOON. 



An Eclipse of the Moon is occasioned by the inter- 
position of the earth between the sun and moon, and 
consequently it must happen when the moon is in op- 
position to the sun, that is, at the full moon, as plate 
XIV. fig. I, 

If the plane of the moon's orbit coincided with the 
plane of the ecliptic, there would be an eclipse at every 
opposition and conjunction; but as that is not the case, 
there can be no eclipse at opposition or conjunction, 
unless at that time the moon be at or near the node. 

The orbit of the moon does not coincide ; for one-half is elevated 
more than 5 degrees and one-third above that of the earth ; and the 
other half is as much below it. Hence she mostly passes either above 
or below the shadow of the earth. 

' The greatest distance from the node at which an 
eclipse of the moon can happen is 12 degrees. When 
she is within that distance, there will be a partial or 
total eclipse, according as a part or the whole disc or 
face of the moon falls within the earth's shadow. If 
the eclipse happen exactly when the moon is full in 
the node, it is called a central or total eclipse. 

The duration of the eclipse lasts all the time the 
moon is passing through the earth's shadow ; and the 
shadow being considerably wider than the moon's di- 
ameter, an eclipse of the moon sometimes lasts three 
or four hours. 

The shadow is also of a conical shape, and as the 
moon's orbit is an ellipse, and not a circle, the moon 
will at different times be eclipsed when she is at differ- 
ent distances from the earth. 



ECLIPSES OF THE SUN. 77 

>nd accordingly as the moon is farther from, or nearer to the earth, 
the eclipse will be of a greater or less duration ; on account of the 
6lower motion of the moon, when more distant from the earth. 

An eclipse of the fnoon always begins on the moon's 
left side, and goes off on her right side. 

This may be conceived by pre-supposing that the earth casts a 
shadow far beyond the moon's orbit ; and as the moon's course is from 
west to east, her eastern edge must necessarily first enter that shadow. 

By knowing exactly at what distance the moon is 
from the earth, and of course the width of the earth's 
shadow at that distance, it is that all eclipses are calcu- 
lated with accuracy for many years before they happen. 

It is found also, that in all eclipses the shadow of the earth is conical, 
which is a demonstration that the body which casts it is of a spherical 
form, for no other sort of figure would, in all positions, cast a conical 
shadow. This is mentioned as another proof that the earth is a spheri- 
cal body. The conical form of the shadow proves also that the sun 
must be a larger body than the earth ; for if two bodies were equal to 
one another (as plate XIV. fig. 3,) the shadow would be cylindrical; 
and if the earth were the larger body (as fig. 14,) its shadow would be 
of the figure of a cone which had lost its vertex. 

ECLIPSE OF THE SUN. 

An Eclipse of the Sun happens when the moon, pass 
ing between the sun and the earth (plate XIV. fig. 2,) 
intercepts the sun's light from coming to the earth, 
which can happen only at the change, or, when the moon 
is in conjunction. 

This may be illustrated by suspending a small globe, or ivory ball, 
in a right line between the eye and the candle. 

The ball intercepting the light of the candle, represents an eclipse 
of the sun ; for as light passes in a right line, the sun is hidden from 
that part of the earth which is under the moon, and therefore he must 
be eclipsed. 

If the whole of the sun be obscured by the body of 

H 



78 ECLIPSE OF THE SUN. 

the moon, the eclipse is total: if only a part be dark- 
ened, it is a partial eclipse ; and so many twelfth 
parts of the sun's diameter as the moon covers, so 
many digits are said to be eclipsed. 

The word digit means a twelfth part of the diameter of either the 
sun or the moon. 

It is only when the moon is in perigee and very 
near one of the nodes, that she can cover the whole disc 
of the sun, and produce a total eclipse ; and no eclipse 
of the sun can happen but when she is within 17 de- 
grees of either of her nodes. At all other new moons 
she passes either above or below the sun, as seen from 
the earth ; and at all other full moons above or below 
the earth's shadow. 

An eclipse of the moon, if central, must be total; 
but an eclipse of the sun may be central and not total. 
Hence there are what are termed annular eclipses, when 
a ring of light appears round the edge of the moon 
during an eclipse of the sun. It has its name from the 
Latin word annulus, " a ring." This kind of eclipse is 
occasioned by the moon being at her greatest distance 
from the earth at the time of an eclipse ; because in 
that situation, those who are under the point of the 
dark shadow will see the edge of the sun, like a fine 
luminous ring, all around the dark body of the moon. 

It is only when the moon is nearest the earth at an 
eclipse of the sun, that the eclipse can be total : a total 
eclipse is, therefore, a very curious and uncommon 
spectacle. Total darkness cannot last more than six 
or seven minutes. 

There must be two solar eclipses in a year, and there 
may be but two. But there may not be one lunar eclipse 



POLAR DAY AND NIGHT, ETC. 79 

in the course of a year. When, therefore, there are 
only two, they are both of the sun. 

There may be three lunar eclipses, and there can be 
no more. There may also be seven eclipses in a year ; 
but in this case, jive will be of the sun, and two of the 
moon. But as there are seven eclipses in the year but 
seldom, the mean number will be about four. 

The ecliptic limits of the sun are greater than those 
of the moon, and hence there will be more solar than 
lunar eclipses, nearly as three to two. But more lunar 
than solar eclipses are seen at any given place, because 
a lunar eclipse is visible to a whole hemisphere at once : 
whereas a solar eclipse is visible only to a part ; and 
therefore there is a greater probability of seeing a lunar 
than a solar eclipse. 



CHAPTER XXIX. 

POLAR DAY AND NIGHT, ETC. 

There being sometimes no night, at other times no 
day, for a while', within the polar circles, is thus ac- 
counted for. The sun being always vertical to some 
one point, and only one at the same time on the globe, 
and shining ninety degrees from that point each way, 
only one complete hemisphere can be at one time il- 
luminated. Therefore, when on the equator, his rays 
must extend to each pole. When he has ad- 
vanced one, two, or ten degrees above the equator, the 
rays must extend the same number of degrees beyond 
the north pole, and consequently be withdrawn as 



80 POLAR DAY AND XIGHT, ETC. 

many from the south pole. And when vertical to the 
tropic of Cancer (23| degrees north of the equator) he 
must shine the same number of degrees on the other 
side of the pole, that is, to the polar, or arctic circle. 

While he thus shines there can be no night within 
that north polar circle, and of course no day within the 
southern polar circle ; for the sun's rays, reaching but 
90 degrees every way, will then extend but to the ant- 
arctic circle. 

For the reasons above given, it is evident that there 
can be but one day and one night at the poles, each half 
a year in length. For, from the moment the sun as- 
cends north of the equator, his rays reach over the pole, 
which he continues to illuminate till he returns to the 
equator, a period of half a year. During this time there 
can be no night at the north pole, nor any day at the 
south pole. 

The reverse of all this, while the sun is south of the equator, maybe 
equally applied to the south pole. The inhabitants of the polar regions, 
however, even when the sun is absent, are not in total darkness ; for 
twilight continues to enlighten them till the sun is 18 degrees below 
their horizon ; and his greatest depression is but b\ degrees more, (23£ 
degrees,) equal to the inclination of the earth's axis. 

Besides this, the moon is above the horizon of the poles a fortnight 
together ; for as she passes through the whole ecliptic monthly, which 
lies one half north, and the other half south of the equator, she must 
continue to shine over one or other of the poles till she returns to the 
equator again. 

A third benefit they receive to mitigate their darkness is, that as the 
moon when at thejkill is ever in the opposite sign to the sun, their win- 
ter full moons must have the highest altitude, describing nearly the 
same track as their summer sun. 

Note. — We say nearly the same track, because the moon mostly va- 
ries a little (sometimes above 5°) from the sun's course in the ecliptic. 

When the sun is in the equator, lie rises exactly 



tJMBRA AND PENUMBRA, IN ECLIPSES. 81 

east, and sets exactly west ; but during the summer 
half year he rises to the north of the cast point, and 
sets as much north of the west ; that is, if he rises 10° 
north of the east, he sets 10° north of the west point, 
&c; the place of his rising varying with his declination. 
During the opposite half year he rises south of the east, 
and sets south of the west. 

It must be observed, that though we say the sun sets as many de- 
grees N. of the W. as it rises N. of the E., &c. yet there will be a small 
variation from sun-rising to sun-setting, as the earth is advancing in its 
orbit. 

This, to some, will be more clearly explained on the globe. If the 
sun were to remain stationary in the ecliptic, from his rising to his set- 
ting, there would be no variation. But the sun advances in the ecliptic 
nearly a degree in 24 hours, which, if correctly allowed for in working 
the problem, will show a small variation between the rising and the 
setting point. Hence, from the shortest to the longest day the sun sets 
rather more towards the north than he rises ; but from the longest to the 
shortest day the variation is more southerly. 



CHAPTER XXX. 

UMBRA AND PENUMBRA, IN ECLIPSES. 

The Umbra and Penumbra in an eclipse may be thus 
explained : (Plate XIV. fig. 5.) Let S be the sun, M 
the Moon, A B or C D, the surface of the earth ; then 
x V z, will be the moon's umbra, in which no part 
of the sun can be seen. The space comprehended 
between the umbra and x ok and z P g, is called the 
penumbra, in which part of the sun only is seen. 

Now it is evident that if A B be the surface of the 
earth, the space between m n, where the umbra falls, 
will suffer a total eclipse ; the parts o m and n P; will 

h2 



82 UMBRA AND PENUMBRA, IN ECLIPSES. 

have a partial eclipse; but to all the other parts of the 
earth there will be no eclipse. 

But as the earth is at different times at different dis- 
tances from the moon, suppose, again, C D to be the 
surface of the earth ; then as the umbra reaches but to 
V, the space within cf will sutler an annular eclipse^ 
and the sun will appear all round about the moon in the 
form of a ring. The parts Jc c dmdfg will have & par- 
tial eclipse, and to the other parts of the earth there 
will be no eclipse. Hence it is evident that in this last 
case, supposing C D the earth, there can be no total 
eclipse anywhere, as the moon's umbra does not reach 
the earth. 

According to M. du Sejour, an eclipse can never be annular longer 
than 12 minutes 24 seconds, nor total longer than 7 minutes 58 seconds. 

The moon's mean motion about the centre of the earth is at the rate 
of about 33' in an hour ; but 33' of the moon's orbit is about 2,280 
miles, which therefore may be considered as the velocity with which 
the moon's shadow passes over the earth ; but this is the velocity upon 
the surface of the earth, only, where the shadow falls perpendicularly 
upon it. In every other place the velocity of the surface will be increased. 

But again, the earth having a rotation about its axis, the relative ve- 
locity of the moon's shadow aver any point of the surface will be even 
different from this. For if the point be moving in the direction of the 
shadow, the velocity of the shadow on that point will be diminished, 
find consequently the time in which the shadow passes over it will be 
increased ; but if the point be moving in a contrary direction to that of 
the shadow (as is the case when the shadow falls on the other side of the 
pole) the time will be diminished. 

From the above it is evident that the length of a solar eclipse at any 
place is affected by the earth's rotation about its axis. 

The different eclipses of the sun may be thus ex- 
plained : let each of the three lower circles (plate XV. 
fig. 3.) represent the earth, and O R its orbit. Let 
each of the three upper circles represent the moon's 



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UMBRA AND PENUMBRA, IN ECLirSES. 83 

penumbra, P U the line described by the centres of 
the moon's umbra and penumbra at the earth ; N the 
moon's node ; E the earth's centre ; p n the moon's 
penumbra; u the umbra. Then in the first position, 
the penumbra^ n just passes by the earth, without fall- 
ing upon it, and therefore there will be no eclipse. In 
the second position, the penumbra p n falls upon the 
earth, but the umbra u does not. In the third position, 
both the penumbra p n and the umbra u fall upon the 
earth ; therefore, where the penumbra falls there will be 
sl partial eclipse, and where the umbra falls there will 
be a total eclipse ; and to the other parts of the earth 
there will be no eclipse. 

As a description of a total eclipse of the sun may be interesting to the 
young reader, we select a few particulars of that which happened April 
22d, 1715. Captain Stannyan, of Berne, in Switzerland, says, " the sun 
was totally dark for four minutes and a half; that a fixed star, and planet, 
appeared very bright ;" J. C. Facis, of Geneva, says, " there was seen, 
during the whole time of the total immersion, a whiteness, which seem- 
ed to break out from behind the moon. Venus, Saturn, and Mercury 
were seen by many. Some persons in the country saw more than six- 
teen stars, and many people on the mountains saw the sky starry as on 
the night of a full moon. The duration of the total darkness was about 
three minutes." 

Dr. J. J. Scheuchzer, at Zurich, says, " that both planets and fixed 
stars were seen ; the birds went to roost ; the bats came out of their holes, 
the dew fell on the grass, and a manifest sense of cold, was experienced. 
The total darkness lasted at Zurich about four minutes." 

Dr. Halley, who observed this eclipse in London, says, " that about 
two minutes before the total immersion, the remaining part of the sun 
was reduced to a very fine horn ; and for the space of about a quarter 
ef a minute, a small piece of the southern horn seemed to be cut ofTfrom 
the rest, and appeared like an oblong star. This appearance could 
proceed from no other cause but the inequalities and elevated parts of 
the moon's surface, by which interposition, part of that exceedingly fine 
filament of light was intercepted. 

" A few seconds before the sun was totally hid, there discovered 



84 THE TRANSIT OF VENUS. 

itself round the moon a luminous ring, in breadth about a digit, or per* 
haps a tenth part of the moon's diameter ; it was of a pale whiteness, or 
rather pearl colour, seeming to me a little tinged with the colours of the 
iris, whence I concluded it was the moon's atmosphere ; for it in all re- 
spects resembled the appearance of an enlightened atmosphere viewed 
from afar, but whether it belonged to the sun or the moon, I shall not 
take upon me to decide. 

" As to the degree of darkness, it was such that one might have ex- 
pected to see more stars than were seen in London. The planets, Jupi- 
ter, Mercury, and Venus, were all that were seen by some ; Capella and 
Aldebaran were also seen. Nor was the light of the ring round the 
moon capable of effacing the lustre of the stars, for it was vastly inferior 
to that of the full moon, and so weak that I did not observe it cast a 
shade. I forbear to mention the chill and damp with which the dark- 
ness of this eclipse was attended ; or the concern that appeared in all 
sorts of animals, birds, beasts, and fishes, upon the extinction of the sun, 
since ourselves could not behold it without emotion." 



CHAPTER XXXI. 

THE TRANSIT OF VENUS. 

The following illustration of the transit of Venus, 
which is an object of great interest and utility, will now 
be understood : 

Let S (plate XIV. fig. 6.) represent the sun, and V 
V Venus at the beginning and end of her transit, as she 
would appear from the earth's centre; also let E E' be 
the corresponding positions of the earth at those times. 

Then, if the observer would be situated at C, the 
centre of the earth, when Venus entered on the solar 
disc, she would appear as a small black spot at s, and 
the true place of both her and the eastern limb of the 
sun would be s. But if the observer were situated 
at any point on the earth's surface, as P, the apparent 



THE TRANSIT OF VENUS. 85 

place of Venus would be at v, and the apparent place 
of the corresponding limb of the sun would be at P ; 
and consequently Venus would appear to the eastward 
of the sun, by a space equal to the arc v p, which is 
the difference of the parallaxes of these two bodies. 

Hence the immersion of Venus would not take place 
so soon to an observer at P as to one at C, by the time 
she would require to describe the apparent arc v P. 

Now, as the transit always must take place at the 
inferior conjunction of the planet, the motions of both 
Venus and the earth will then be from east to west, 
while the motion of the earth on its axis is in a con- 
trary direction. 

Consequently, while Venus and the earth move in 
their orbits from V to V, and from E to E', the point 
P, which at the commencement of the motion was west 
of the centre, will at the end of it be on the east of it, 
as at P'. Hence the observer, who was supposed to be 
situated at C, would perceive Venus just leaving the 
sun's disc, and her apparent place would be s'; while 
to the observer at P', her apparent place would be at v\ 
and that of the sun's western limb at P, The apparent 
distance of Venus from the sun at the end of the transit 
is therefore the arc v' P, which is equal to the differ- 
ence of the parallaxes of the sun and Venus, as before. 

Consequently the time of the duration, as observed at 
the point P, will be Zessthan the absolute duration, by 
the time which the planet would require to describe the 
two apparent arcs v P and v' P, or twice the difference 
of the parallaxes of the sun and the planet. 

The principal use to which astronomers apply the 



86 OCCULTATIOtf OF THE FIXED STARS. 

transits of Venus is in determining the distance of the 
sun from the earth by means of his parallax, which, on 
account of its smallness, they have in vain attempted * 
to ascertain by various other methods. 

These transits are also applied with great effect in ascertaining the 
longitude of places ; in correcting the elements of the planets, especi- 
ally the places of the aphelia, the situation of the nodes, and the incli- 
nations of the orbits. 

The transits of Mercury take place much oftener than those of Venus ; 
but on account of his greater distance from the earth, and the small- 
ness of his parallax from the sun, they are not susceptible of equal 
utility with those of Venus, except for the determination of terrestial 
longitude, for which they are superior. 

OCCULTATION OF THE FIXED STARS. 

Nearly related to eclipses of the sun, is the occulta- 
Hon of the fixed stars, which implies the obscuration 
of these heavenly bodies by the moon or a planet. 

The only method of ascertaining whether an occul- 
tation will happen, is that of calculating the place of 
the moon at the ecliptic conjunction. The course of 
the moon, however, affords limits to these occurrences, 
which enable astronomers to judge when they will take 
place ; for Cassini has remarked that all stars whose 
latitudes do not exceed 6° 36' either north or south, 
may suffer an occultation on some part of the earth ; 
and if the latitudes are not more than 4° 32', the occul- 
tation may happen on any part of the earth. 

By conjunction is meant having the same longitude ; or answering 
to the same degree of the ecliptic. 

By latitude of a star (as has been shown in page 49) is meant its 
distance from the ecliptic, either north or south. 

To determine when these eclipses or occultations 
will happen, we must compute the time of the con- 
junction, and the true latitude of the moon at that epoch; 






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THE HARVEST MOOX. 87 

and then, if the difference of the latitudes of the moon 
and the star exceed 1° 20', there cannot be any occup- 
ation ; but if this difference be less than 51', there 
must be an eclipse of the star on some part of the 
earth : between these limits the occultation may or 
may not take place. 

In very different places of the earth, a great difference will result 
from the change in the moon's parallax, and this difference may be even 
so great as altogether to prevent the obscuration from taking placa 



CHAPTER XXXII. 

THE HARVEST MOON. 

Owing to the daily progress the Moon is making in 
her orbit from west to east, she rises about 50 minutes 
later every day, when near the equator, than on the 
day preceding. But in places of considerable latitude 
there is a remarkable difference, especially about the 
time of harvest, when at the season of full moon she 
rises to us for several nights together only from 17 to 
25 minutes later on the one day than on that immedi- 
ately preceding. 

To those who live in the latitude of London, when the moon is in 
the 10th of Pisces, she rises 25 minutes later than en the day pre- 
ceding ; the 23d of Pisces, 20 minutes later ; the 7th of Aries, 17 minutes 
later ; the 20th, 17 minutes ; the 3d of Taurus, 20 minutes ; and the 
16th, 24 minutes later. 

To persons who live at considerable distances from 
the equator, the autumnal full moon rises very soon af- 
ter sun-set for several nights together ; and by thus 
succeeding the sun before the twilight is ended, the 
moon prolongs the light, to the great benefit of those 



88 THE HARVEST MOON. 

that are engaged in gathering in the fruits of the earth. 
Hence the full moon at this season is called the Har- 
vest Moon. 

It is believed that this was observed by persons engaged in agricul- 
ture at a much earlier period than that in which it was noticed by as- 
tronomers. The former ascribed it to the goodness of the Deity, not 
doubting but that he had so ordered it for their advantage. 

About the equator, where there is no such variety 
of seasons, and where the weather changes but seldom, 
and at stated times, moonlight is not wanted for gather- 
ing the fruits of the earth, and there the moon rises 
throughout the year at nearly the equal intervals of 50 
minutes, as before observed. 

At the polar circles, the autumnal full moon rises at 
sun-set, from the first to the third quarter ; and at the 
poles, where the sun is for half a year absent, the win- 
ter full moons shine constantly without setting, from 
the first to the third quarter. 

The moon's path may be considered as nearly coin- 
ciding with the ecliptic ; and all these phenomena are 
owing to the different angles made by the horizon and 
different parts of the moon's orbit, or in other words, 
by the moon's orbit lying sometimes more oblique to 
the horizon than at others. In the latitude of London, 
as much of the ecliptic rises about Pisces and Aries in 
two hours as the moon goes through in six days ; there- 
fore while the moon is in these signs, she differs but 
two hours in rising for six days together, that is, one 
day with another, about 20 minutes later every day than 
on the preceding. 

These parts or signs of the ecliptic which rise with 
the smallest angles, set with the greatest, and vice versa- 



THE HARVEST MOON. 89 

And whenever this angle is least, a greater portion of 
the ecliptic rises in equal times than when the angle is 
larger. This may be seen by elevating the pole of 
the globe to any considerable latitude, and then turning 
it round on its axis. 

Consequently when the moon is in those signs which rise or set with 
the smallest angles, she rises or sets with the least difference of time ; 
and on the contrary, with the greatest difference in those signs winch 
rise or set with the greatest angles. 

Let plate XV. fig. 2, represent the globe, the north pole being ele- 
vated to about 5H°, with Cancer on the meridian, and Libra rising in 
the east. In this position the ecliptic has a high elevation, making an 
angle with the horizon of 62°. 

But let the globe be turned half round on its axis till Capricorn 
comes to the meridian, and Aries rises in the east, then the ecliptic 
will have the low elevation, above the horizon (fig. 2,) making an angle 
of only 15° with it. This angle is 47° less than the former angle, equal 
to the distance between the tropics. 

In northern latitudes, the smallest angle made by the 
ecliptic and horizon is when Aries rises, at which 
time Libra sets ; the greatest when Libra rises, at which 
time Aries sets. The ecliptic rises fastest about Aries, 
and slowest about Libra. Though Pisces and Aries 
make an angle of only about 15° with the horizon when 
they rise, to those who live in the latitude of London 
they make an angle of 62° with it xchen they set. The 
Moon, quitting Pisces and Aries, arrives in about four- 
teen days at the opposite signs, Virgo and Libra, and 
then she differs almost four times as much in rising ; 
being one hour and about fifteen minutes later every 
day or night than on the preceding. 

Those who are acquainted with the globes will easily demonstrate 
this problem by putting small patches on the ecliptic, at distances from 
each other equal to the moon's daily course ; which (deducting for the 
sun's advance) is little more than 12°. Then (after rectifying the globe 

i 



90 THE HARVEST MOOS. 

for the latitude, and setting the hour-index to 12,) by turning the globe 
round, and observing the time of the appearing and disappearing of the 
patches, the variation in the time of the moon's rising or setting will be 
shown on the hour circle. 

As the moon can never be full but when she is op 
posite to the sun, and the sun is never in Virgo or Li 
bra but in our autumnal months, September and Octo 
ber, it is evident that the moon is never full in the op 
posite signs, Pisces and Aries, but in those two months 
Therefore we can have only two full moons in a year, 
which rise, for a week together, very near the time of 
sun-set. The former of these is called the Harvest 
Moon, and the latter the Hunter's Moon. 



CHAPTER XXXIII. 

THE HARVEST MOON, CONTINUED. 

Though there are but two full moons in the year 
that rise with so little difference of time, yet the phe- 
nomenon of the moon's rising for a week together so 
nearly in point of time, occurs every month, in some 
part or other of her course. 

In Winter the signs Pisces and Aries rise about noon ; and the sun, 
in Capricorn, is then only a quarter of a circle distant. Therefore the 
moon, while passing through them, must be only in her first quarter 
Hence her rising is neither regarded nor perceived. 

In Spring, these signs rise with the sun, because he is then in them , 
and as the moon changes while passing through the same sign with the 
sun, it must then be the change, and hence invisible. 

In Summer, they rise about midnight, for the sun being three signs, 
or a quarter of a circle before them, the moon is in them, or about her 
third quarter. Hence rising so late, and giving but little light, her rising 
passes unobserved. 



THE IIAKVEST MOON. 91 

The moon goes round the ecliptic in 27 days, 8 hours ; 
but not from change to change in less than 29 days, 12 
hours; so that she must be once in every sign, and 
ticice in some one sign every Junation. 

If the earth had no annual motion, every new moon would fall in 
the same sign and degree of the ecliptic ; and every full moon in the 
opposite : for the moon would go exactly round the ecliptic from change 
to change. So that if she were once full in any sign, suppose in Pisces 
or Aries, she would always be full there. 

But in the time the moon goes round the ecliptic from any conjunc- 
tion or opposition, the earth goes 27£ degrees, that is, almost a sign for- 
ward ; so that the moon must go 27£ degrees more than round, before 
she can be in conjunction with or opposite to the sun again. Hence, 
if she were in her conjunction at the first degree of Aries, she would, in 
one lunation, not only return to the same point, but repass it, and go 
twice over Aries to the 27£- degree. 

To the inhabitants at the equator the north and south 
poles appear in the horizon ; and therefore the ecliptic 
makes the same angle southward with the horizon when 
Aries rises, as it does northward when Libra rises ; con- 
sequently she rises and sets not only at nearly equal 
angles with the horizon, but at the equal distance in 
time of about 50 minutes, all the year round : and hence 
there can be no particular harvest moon about the 
equator. 

The farther any place is from the equator, if it be 
not beyond the polar circles, the angle which the eclip- 
tic and the horizon make gradually diminishes when 
Pisces and Aries rise. 

This the globe itself will fully illustrate ; for the more the north 
pole is elevated, the more nearly does the ecliptic coincide with the 
horizon ; that is, the angle is diminished. 

Though in northern latitudes the autumnal full 
moons are in Pisces and Aries ; yet in southern lati- 



92 LEAr-YEAR. 

tudes it is just the reverse, because the seasons are the 
contrary : for Virgo and Libra rise at as small angles 
with the horizon in southern latitudes, as Pisces and 
Aries do in the northern : and therefore the harvest 
moons are just as regular on one side of the equator as 
on the other. 

In this illustration of the harvest moon, we have supposed the moon 
to move i?i the ecliptic, from which the sun never deviates ; but the 
orbit in which the moon really moves (as was noticed under the article 
Eclipses) is different from the ecliptic ; one half being elevated 5£ de- 
grees above it, and the other half as much depressed below it. And 
this oblique motion causes some small difference in the time of her 
rising and setting from what has been above mentioned. 

At the polar circles, the full moon neither rises in 
summer, nor sets in winter. For the winter full moon 
being as high in the ecliptic as the summer sun, she 
must therefore continue, while passing through the 
northern signs, above the horizon ; and the summer 
full moon being as low in the ecliptic as the winter sun, 
can no more rise, when passing through the southern 
signs, than he does. 



CHAPTER XXXIV. 

OF LEAP-YEAR. 

The time our earth takes to make one complete re- 
volution, in its orbit round the sun, we call a year. To 
complete this with great exactness is a work of consi- 
derable difficulty. It has mostly been divided into 
twelve months of 30 days. 






/'/„/, // 




LEJP-YEAK. 93 

The ancient Hebrew months consisted of 30 days each, except the 
last, which contained 35. Thus the year contained 3G5 days. An in- 
tercalary month at the end of 120 years supplied the difference. 

The Athenian months consisted of 30 and 29 days alternately, ac- 
cording to the regulation of Solon. This calculation produced a year 
of 354 days, and a little more than one-third. But as a solar month 
contains 30 days, 10 hours, 29 minutes, Meton, to reconcile the differ- 
ence between the solar and lunar year, added several embolismic, or 
intercalary months, during a cycle, or revolution of 19 years. 

The Roman months, in the time of Romulus, were only ten of 30 
and 31 days. Numa Pompilius, sensible of the great deficiency of this 
computation, added two more months, and made a year of 355 days. 

The Egyptians had fixed the length of their year to 365 days. 

Julius Caesar, who was well acquainted with the 
learning of the Egyptians, was the first who attained to 
any accuracy on the subject. Finding the year esta- 
blished by Numa ten days shorter than the solar year, 
he supplied the difference, fixed the length of the year 
to be 365 days, 6 hours, and regulated the months ac- 
cording to the present measure. To allow for the six 
odd hours, he added an intercalary day every fourth 
year to the month of February, reckoning the 24th of 
that month twice, which year must of course consist of 
366 days, and is called Leap-year. From him it was 
denominated the Julian year. 

This year is also called Bissextile in the Almanacs, 
and the day added is termed the intercalary day. 

The Romans, as has been observed, inserted the intercalary day, by 
reckoning the 24th twice, and because the 24th of February in their 
calendar was called sexta calendas Martii, the sixth of the calends of 
March, the intercalary day was called bis sexta calendas Martii, the 
second sixth of the calends of March, and hence the year of intercalation 
had the appellation of Bissextile. We introduce in leap-year a new 
day in the same month, namely, the 29th. 

To ascertain at any time what year is leap-year, 

i 2 



94 LEAP-YEAR. 

divide the date of the year by 4, if there is no remain- 
der it is leap-year. Thus 1824 was leap-year. But 
1825 divided by 4, leaves a remainder of 1, showing 
that it was the first year after leap-year; and as 1829, 
divided by 4, leaves 1, it will be the first after leap- 
year. 

But the true solar year does not contain exactly 365 
days, 6 hours, but 365 days, 5 hours, 48 minutes, and 
49 seconds ; which to calculate for correctly, requires 
an additional mode of proceeding : 365 days, 6 hours, 
exceeds the true time by 11 minutes, 11 seconds, every 
year, amounting to a whole day in a little less than 130 
years. 

Notwithstanding this, the Julian year continued in 
general use till the year 1582, when Pope Gregory 
XIII. reformed the calendar, by cutting off ten days be- 
tween the 4th and 15th of October in that year, and 
calling the 5th day of that month the 15th. This al- 
teration of the style was gradually adopted through the 
greater part of Europe, and the year was afterwards 
called the Gregorian year, or New style. 

In this country, the method of reckoning according to 
the New style was not admitted into our calendars until 
the year 1752, when the error amounted to nearly 11 
days, which were taken from the month of September, 
by calling the 3d of that month the 14th. 

The error amounting to one whole day in about 130 
years (by making every fourth year leap-year,) it is settled 
by an act of parliament that the year 1800, and the year 
1900, which, according to the rule above given, are 
leap-years, shall be computed as common years, having 



THE TIDES. 96 

only 365 clays in each ; and that every four hundredth 

year afterwards shall be a common year also. 

If this method be adhered to, the present mode of reckoning will not 
vary a single day from true time in less than 5,000 years: 

The beginning of the year was also changed, by the 
same act of parliament, from the 25th of March to the 
1st of January. So that the succeeding months of Ja- 
nuary, February, and March, up to the 24th day, which 
would, by the Old style, have been reckoned part of 
the year 1752, were accounted as the first three months 
of the year 1753. Hence we see such a date as this, 
January 1, 1757-8, or February 3, 1764-5 ; that is, ac- 
cording to the Old style it was 1764, but according to 
the New, 1765, because now the year begins in Janua- 
ry instead of March. 



CHAPTER XXXV. 

THE TIDES. 

The oceans, which cover more than one half of the 
globe, are in continual motion ; they ebb and flow per- 
petually, and these alternate elevations and depressions 
are called the tides, or the flux and reflux of the sea. 

The ancients considered the ebbing and flowing of the tides as one 
of the greatest mysteries in nature, and were utterly at a loss to ac- 
count for it. Galileo and Descartes, and particularly Kepler, made 
some successful advances towards ascertaining the cause ; but Sir Isaac 
Newton was the first who clearly pointed out the phenomenon, and 
showed what were the chief agents in producing these motions. 

The tides are not only known to be dependent upon 
some fixed and determinate laws ; but the true cause 



96 THE TIDES. 

of their agitation is demonstrated to be the attraction 
of the sun and moon, particularly the latter ; for as she 
is so much nearer the earth than the sun, she attracts 
with much greater force than he does, and consequently 
raises the water much higher ; which, being a fluid, 
loses, as it were, its gravitating power, and yields to 
their superior force. 

That the tides are dependant upon some known and determinate 
laws, is evident from the exact time of high water being previously 
given in every ephemeris, and in many of the common almanacs. 

The moon comes every day later to the meridian than on the day 
preceding, and her exact time is known by calculation ; and the tides 
in any and every place, will be found to follow the same rule ; hap- 
pening exactly so much later every day as the moon comes later to the 
meridian. From this exact conformity to the motions of the moon, we 
are induced to look to her as the cause ; and to infer that those phe- 
nomena are occasioned principally by the moon's attraction. 

If the earth were at rest, and there were no influence 
from either sun or moon, it is obvious from the princi- 
ples of gravitation, that the waters in the ocean would 
be truly spherical, as plate XVI. fig. 1 ; but daily expe- 
rience proves that they are in a state of continual agi- 
tation. 

If the earth and moon were without motion, and the 

earth covered all over with water, the attraction of the 

moon would raise it up in a heap in that part of the 

ocean to which the moon is vertical, and there it would, 

probably, always continue, as plate XVI. fig. 2 ; but 

by the rotation of the earth upon its axis, each part of 

its surface to which the moon is vertical is presented 

to the action of the moon, and thus are produced two 

floods, and two ebbs. 

In this supposition we have omitted to take notice of the sun's in- 
fluence. 



THE TIDES. 97 

The attractive power of the sun is to that of the moon 
as three to ten ; hence, when the moon is at change, 
the sun and moon being in conjunction, or on the same 
side of the earth, the action of both bodies is on the 
same ocean of waters ; the moon raising it ten parts, 
and the sun three, the sum of which is thirteen parts, 
represented by plate XVI. fig. 4. Now it is evident 
that if thirteen parts be added to the attractive power 
of these bodies, the same number of parts must be drawn 
off from some other parts, as at C and D. It will now 
be high water under the moon at A, and low water at 
C and D. 

The attractive power of the sun, according to some authorities, is to 
that of the moon as two to ten, or one-fifth, and according to others as 
one-third. 

Those parts of the earth where the moon appears in 
the horizon, as at C and D, will have low water ; for 
as the waters in the zenith and nadir (A and B) rise at 
the same time, the waters adjacent will press towards 
those places to maintain the equilibrium ; and to sup- 
ply the place of those, others will move the same way, 
and so on ; hence at the places 90° distant (C and D) 
the waters will be lowest. 

It is evident that, the quantity of water being the same, a rise cannot 
take place at A and B, without the parts C and D being at the same 
time depressed \ and in this situation the waters may be considered as 
partaking of an oval form. 



98 THE TIDES. 

CHAPTER XXXVI. 

THE TIDES, CONTINUED. 

It has been already shown, under the article grayi 
tation, that the power of gravity diminishes as the square 
of the distance increases ; therefore not only those parts 
of the sea immediately below the moon must be attract- 
ed towards it, and occasion the flowing of the tides 
there, as at A, fig. 4 ; but a similar reason occasions 
the flowing of the tides in the nadir, or that part of the 
earth diametrically opposite to it, as at B ; for in the 
hemisphere farthest from the moon, the parts being 
less attracted than those which are nearer, gravitate 
less towards the earth's centre, and consequently must 
be higher than the rest ; and as every portion of the 
earth will pass twice through the elevated, and twice 
through the depressed parts, two tides will be produced 
each day. 

It has been otherwise thus explained : All bodies moving in circles 
have a tendency to fly off from their centres ; now as the earth and 
moon move round the centre of gravity, that part of the earth which is 
at any time turned from the moon, would have a greater centrifugal 
force than the side next her. At the earth's centre, the centrifugal 
force will balance the attractive force ; therefore as much water is 
thrown off by the centrifugal force on the side which is turned from 
the moon, as is raised on the side next her by her attraction. 

If the tide be at high water mark in any point or har- 
bour that lies open to the ocean, it will presently sub- 
side and flow back for about six hours, and then return 
in the same time to its former situation, rising and fall- 
ing nearly twice a day, or in the space of somewhat 
more than twenty-four hours. 

The interval, however, between its flux and reflux 



THE TIDES. 99 

is not precisely six hours, but about 12 minutes and % 
more, so that the time of high water does not happen 
at the same hour, but is above f of an hour later evevy 
day for about 30 days, when it again recurs as before. 
If the moon were stationary, there would be two tide^ 
every twenty-four hours, but as that body is daily pro- 
ceeding from west to east in her orbit above 12°, the 
earth must make more than a complete revolution on 
its axis, before the same meridian is in conjunction 
with the moon. And hence, every succeeding day the 
time of high water will be above % of an hour later 
than on the preceding. 

For example : If it be high water to day at noon, it will be low wa- 
ter at 12 and £ minutes after six in the evening ; and, consequently, 
after two changes more, the time of high water the next day will be 
above £ of an hour after noon : the day following above £ past one ; — 
the day after that above £ past two, and so on. 

Again : Suppose at any place it be high w T ater at three in the after- 
noon upon the day of the new moon, the following day it will be high 
w r ater about £ after three ; — the day after about £ past four, and so on 
till the next new moon. 

4 Not only when the sun and moon are in conjunction, 
or at the change, but when in opposition, at the fully 
the tides are at the highest, as in fig. 6. For when the 
moon is at full, ten parts of water are raised from that 
side of the earth next her, by her attractions ; and as 
the side which is next her is opposite to the sun, three 
parts must be thrown off by his centrifugal force, the 
sum of which will be thirteen parts next the moon. — 
Again, from the side opposite to the moon and under 
the sun, ten parts are thrown off by her centrifugal force, 
and three raised by his attraction, making thirteen, the 
same as before. 



100 THE TIDES. 

If there were no moon, the sun, by his attraction, would raise a 
small tide on the side of the earth next him ; and it is evident that the 
tides on the opposite side would be raised as high by the centrifugal 
force ; for the sun and earth, as well as the earth and moon move round 
their centres of gravity. 

The highest tides happen when the sun and moon 
are either in conjunction (fig. 4,) or opposition (fig. 6,) 
and these are called Spring Tides ; but when the moon 
is in her quarters (as fig. 5,) the influences of the sun 
and moon counteract each other ; that is, they act in 
different directions ; the attraction of the one raising 
the waters, while that of the other depresses them. The 
moon of herself would raise the water ten parts under 
her, but the sun, being then in a line with low water, 
his influence keeps the tides from falling so low there, 
and consequently from rising so high under and oppo- 
site the moon. His power, therefore, on the low water 
being three parts 9 leaves only seven parts for the high 
water, under and opposite the moon. These are called 
Neap Tides. 



CHAPTER XXXVII. 
THE TIDES, CONTINUED. 

The tides are known to rise higher at some seasons 
than at others : for the moon goes round the earth in an 
elliptic orbit, and therefore she approaches nearer to 
the earth in some parts of her orbit than at others. 
When she is nearest, the attraction is the strongest, 
and consequently it raises the tides most : and when 



THE TIDES. 101 

she is farthest from the earth, her attraction is the least, 
and the tides are the lowest. 

From the above theory, it may be supposed that the 
tides are at the highest when the moon is on the meri- 
dian, or due north and south. But we find that in open 
seas, where the water flows freely, the moon has gene- 
rally passed the north or south meridian about three 
hours, when it is high water. For even if the moon's 
attractions were to cease when she had passed the meri- 
dian, the motion of ascent communicated to the water 
before that time, would make it continue to rise for 
some time after. 

Much more must it do so when the attraction is not withdrawn, but 
only diminished : as a little impulse given to a moving ball will cause 
it to move still farther than it otherwise could have done. And expe- 
rience shows that the heat of the day is greater at three o'clock in the 
afternoon than it is at twelve ; and it is hotter in July and August than 
in June, because of the increase made to the heat already imparted. 

The tides, however, answer not always to the same 
distance of the moon from the meridian, at the same 
place ; but are variously affected by the action of the 
sun, which brings them on sooner, when the moon is in 
hex first and third quarters ; and keeps them back later, 
when she is in her+pecond and fourth. Because in the 
former case the tide raised by the sun alone would be 
earlier than the tide raised by the moon, and in the 
latter case later. 

The greatest spring tide will happen when the moon 
is in perigee, if other things are the same ; and the suc- 
ceeding spring tide when the moon is in apogee will 
be the least. But as the effect of a luminary is greater 
the nearer it approaches to the plane of the equator, 

K 



102 THE TIDES. 

and as the earth is nearer the sun in winter than in 
summer, and still nearer in February and October than 
in March and September ; the greatest tides happen not 
till some time after the autumnal equinox, and return a 
little before the vernal. 

In open seas the tides rise but to very small heights, 
in proportion to what they do in wide-mouthed rivers 
opening in the direction of the stream of tide. For in 
channels growing gradually narrower, the water is ac- 
cumulated by the contracting banks. At the mouth 
of the Indus, the water rises and falls full thirty feet, 
and in the bay of Fundy seventy feet. 

The tide in the above instance has been compared to a moderate 
wind, which, though not much felt in an open plain, may yet appear 
with a strong and brisk current in a street, and become still more pow- 
erful as the more confined. 

Though the tides in open seas are at the highest about 
three hours after the moon has passed the meridian, 
yet the waters, in their passage through shoals and 
channels, and by striking against capes and head lands, 
are so retarded that, to different places, the tides hap- 
pen at all distances of the moon from the meridian, 
consequently at all hours of the lunar day. 

The tide raised by the moon in the German Ocean, when she is 
three hours past the meridian, takes twelve hours to come thence to 
London bridge, where it arrives by the time that a new tide is raised 
in the ocean. 

There are no tides in lakes, because they are gene- 
rally so small that, when the moon is vertical, she at- 
tracts every part of them alike, and by rendering all 
the waters equally light, no part of them can be raised 



THE TIDES. 103 

higher than another. The Mediterranean and Baltic 
seas have v^ry small elevations, because the inlets by 
which they communicate with the ocean are so narrow, 
that they cannot, in so short a time, either receive or 
discharge enough, sensibly to raise or sink their sur- 
faces. 

Air being lighter than water, it cannot be doubted that the moon 
raises much higher tides in the air than in the sea. 

Although it has been stated that the highest tides 
are produced by the conjunction and opposition of the 
sun and moon, yet their effects are not immediate; the 
highest tides happen not on the days of the full and 
change, neither do the lowest tides happen on the days 
of their quadratures. But on account of the continua- 
tion of motion these effects are greatest and least, 
some time after their forces are. So that the -greatest 
spring tides commonly happen two days after the new 
and full moons ; and the least neap tides two days 
after the first and third quarters. 

For if the greatest elevation immediately under the moon, points to 
one side of the equator, the opposite greatest elevation points as much 
to the other side. And those places which are on the same side of the 
equator with the luminary, approach nearest to the greatest elevation 
when she is above the horizon, than to the greatest opposite elevation 
when she is below the horizon. 

This inequality is greatest when the sun and moon 
have the greatest declination. It is also greatest in 
places most remote from the equator. The nearer the 
place approaches to the poles, the farther it is removed 
from the greatest elevation on the opposite side of the 



104 THE PRECESSION OF THE EQUINOX. 

equator. Thus the less tide is continually diminishing, 
till at last it entirely vanishes, and leaves only one tide 
in the day. 

Hence it is found by observation, that there is only 
one tide in twenty-four hours, in all places in the polar 
regions in which the moon is either always above or 
always below the horizon, during the whole rotation 
of the earth about its axis 



CHAPTER XXXVIII. 

THE PRECESSION OF THE EQUINOX. 

It has been already observed, that the form of the 
earth is that of an oblate spheroid ; for by the earth's mo- 
tion on its axis there is more matter accumulated all 
around the equatorial parts than any where else on the 
earth. 

The sun and moon by attracting this redundancy of 
matter bring the equator sooner under them, in every 
return towards it, than if there were no such accumula- 
tion. Therefore if the sun sets out from any star, or 
other fixed point in the heavens, the moment when he 
is departing from the equinoctial (or from either tropic) 
he will come to the same equinox (or tropic) again 20 
minutes, 17i seconds of time (or which is equal to 50" 
of a degree) before he arrives at the same fixed star or 
point from which he set out. For the equinoctial 
points recede 50" of a degree westward every year, 
contrary to the sun's annual progressive motion. 



THE PRECESSION OF THE EQUINOX. 105 

To prove that 20 minutes 17* seconds of time are equal to 50" of a 
degree, it must be recollected that the sun goes through the whole 
ecliptic of 360°, in 365} days, which is not quite one degree each day, 
but 59' 8", (or 52" less than a degree.) Therefore, if by the rule of pro- 
portion we say, as 59' 8": 24 hours: : 50", the result will be 20 minutes 
17£ seconds, nearly. That the sun has a daily apparent motion in the 
ecliptic from w T est to east is evident from comparing the sun's right 
ascension every day with that of the fixed stars lying near him. For 
the sun is found constantly to recede from those on the west, and ap- 
proach those on the east ; hence his apparent annual motion is found to 
be from west to east. 

When the sun arrives at the same equinoctial or sol- 
stitial point, he finishes what is called the tropical 
year; which, according to some authorities, is found to 
contain 365 days, 5 hours, 48 minutes, 48 seconds (see 
page 4,) and when he arrives at the same star again, 
as seen from the earth, he completes the sidereal year, 
which contains 365 days, 6 hours, 9 minutes, 14^ se- 
conds. The sidereal year is therefore 20 minutes, \1\ 
seconds longer than the solar or tropical year, and 9 
minutes, 14 \ seconds longer than the Julian or civil 
year, which is 365 days, 6 hours. So that the civil 
year is almost a mean between the sidereal and tropical. 

According to Professor Vince, a sidereal year is 365 days, 6 hours, 9 
minutes, 11 seconds, .5; and a tropical year 365 days, 5 hours, 48 mi 
nutes, 48 seconds. 

As the sun describes the whole ecliptic, or 360° in 
a tropical year, he moves 59' 8" of a degree every day 
at a mean rate ; which is equal to 50 seconds of a de- 
gree in 20 minutes 17^ seconds of time : therefore he 
will arrive at the same equinox or solstice when he is 
50" of a degree short of the same star or fixed point in 
the heavens, from which he set out the year before. So 
that, with respect to the fixed stars, the sun and equi- 

K 2 



106 THE PRECESSION OF THE EQUINOX. 

noctial points fall back (as it were) 30° "in 2,160 years. 
This will make the stars appear to have gone 30° for- 
ward, with respect to the signs in the ecliptic in that 
time : for it must be observed, that the same signs al- 
ways keep in the same points of the ecliptic, without re- 
gard to the place of the constellations, 

50" short in one year are = 1° short in 72 years. For in a degree 
are (60 x 60) 3,600", which divided by 50", will give 72.— And 1° less 
in 72 years = 30° or one whole sign in 2,160 years. To explain this by 
a figure ; suppose the sun (plate XVII. fig. 1st,) to have been in con- 
junction with a fixed star at S, on the first degree of Taurus, 342 years 
before the birth of Christ, or about the 15th year of Alexander the 
Great ; then making 2,160 revolutions through the ecliptic, he will 
still be found at the end of so many sidereal years, again at S : but at 
the end of so many Julian years, he will be found at J, and at the end 
of so many tropical years, at T. in the 1st degree of Aries, which has 
receded hack from S to T in that time, by the precession of the equi- 
noctial points op and ^=. The arc S T will be equal to the amount of 
the precession of the equinox in 2,160 years, at the rate of 50" of a de- 
gree, or 20 minutes 17? seconds of time annually, as above calculated 

From the shifting of the equinoctial points, and with 
them all the signs of the ecliptic, it follows that the 
longitude of the stars must continually increase. Hence 
those stars which, in the infancy of astronomy, were in 
Aries, are now got into Taurus; those of Taurus into 
Gemini, as may be seen by inspecting the celestial 
globe. Hence likewise it is that the star which rose 
or set at any particular time of the year, in the times 
of Hesiod, Eudoxus, Virgil, Pliny, &c. by no means 
answers at this time to their descriptions. 

By comparing the longitude of the same stars, at different times, the 
motion of the equinoctial points, or the precession of the equinoxes may 
be found. 

Hipparchus was the first person who observed this motion, by com- 
paring his own observations with those which Timocharis made 155 



pa t/c W6 



Plate 15 



Epicycloids 




Musti'dtion of the Harvest Moon 




PRECESSION OF THE EQUINOX. 107 

years before. From this he judged the motion to bo about 1° in about 
100 years ; but he doubted whether the observations of Timocharis 
were sufficiently accurate. — In the year 128 before Christ he found the 
longitude of Virgin's Spike to be 5 signs 24°, and in the year 1750 its 
longitude was found to be 6 s. 20° 21'. In the same year he found the 
longitude of the Lion's Heart to be 3 s. 29° 50\ and in 1750, it was 4 s. 
26° 21'. The mean of these gives 50". 4 in a year for the preoession. 
By comparing the observations of Albategnius, in the year 878, with 
those made in 1738, the precession appears to be 51" 9'". — From a com- 
parison of fifteen observations of Tycho, with as many made by M. de 
la Caille, the precession was found to be about 50" 20'". 

By proceeding to shift a whole degree every 72 years, 
and a whole sign every 2160 years, the equinoctial 
points will fall back through the whole of the 12 
signs, and return to the same points again in 25,920 
years ; which number of years completes the grand ce- 
lestial period. 

From the creation to the year 1819, supposing it to be (4004 -|- 1819> 
•== 5823 years, the equinoctial points have receded 2 s. 20° 51' 54". 



CHAPTER XXXIX. 

THE PRECESSION OF THE EQUINOX, CONTINUED. 

Having thus noticed the cause of the precession of 
the equinoctial points, which occasions a slow deviation 
of the earth's axis from its parallelism, and thereby a 
change of the declination of the stars from the equator, 
together with a slow apparent motion of the stars for- 
ward, with respect to the signs of the ecliptic, the 
phaenomena may be explained by a diagram. 

Let S O N A (fig 3, plate XVII.) be the axis of the 
earth produced to the starry heavens, and terminating 
in A, the present north pole in the heavens ; EOQ 



108 PRECESSION OF THE EQUINOX. 

the equator ; T 25 Z the tropic of Cancer, and VTK5 1 
the tropic of Capricorn ; VOZ the ecliptic, and B O 
its axis, both which are immoveable among the stars. 
But as the equinoctial points recede in the ecliptic, 
the earth's axis S O N is in motion upon the earth's 
centre O, in such a manner as to describe the cone N 
O w, and S O 5, round the axis of the ecliptic B O, 
in the time the equinoctial points move round the 
ecliptic, which is 25,920 years. 

In that length of time the north pole of the earth's 
axis produced, describes the circle A B C D A in the 
heavens, round the pole of the ecliptic, which keeps 
immoveable in the centre of that circle. The earth's 
axis being 23^° inclined to the axis of the ecliptic, 
the -circle A B C D A, described by the north pole of 
the earth's axis, produced to A, is 47° in diameter, or 
double the inclination of the earth's axis. 

In consequence of this motion, the point A, which 
is at present the north pole of the heavens, and near to 
a star of the second magnitude in the tail of the con- 
stellation called the Little Bear, must be deserted by 
the earth's axis. And this axis moving backward a 
degree every 72 years, will be directed towards the 
star or point B in 6,480 years from this time : and in 
twice that time, or 12,960 years, it will be directed 
towards the star or point C, which will then be the 
north pole of the heavens ; although it is at present 8i° 
south of the zenith of London, L. 

Then the present positions of the equator and the 
tropics represented by the black lines, will be changed 
to those represented by the dotted lines* And the sun, 



OBLIQUITY OF THE ECLIPTIC, ETC. 109 

which in the diagram is over Capricorn, and makes the 
shortest days and longest nights to the northern hemi- 
sphere, will then be over Cancer, and make the days 
longest and nights shortest. 

It will then require 12,960 years more (or 25,920 
from this time) to bring the north pole back quite round 
to the present point : and then, and not till then, will 
the same stars which now describe the equator, tropics, 
polar circles, &c. describe them again. 



CHAPTER XL. 

THE OBLIQUITY OF THE ECLIPTIC, ETC. 

It may not be amiss to mention the method used by 
astronomers to determine the obliquity of the ecliptic ; 
which is, by taking half the difference of the greatest 
and least meridian altitudes of the sun. 

Eratosthenes, 230 years before Christ, found 

the obliquity to be 
Ptolemy, 140 years after Christ 
Copernicus, in 1500 
M. De la Lande, in 1768 
Not to mention many others ; and from all these united observations, 
it is manifest that the obliquity of the ecliptic continually decreases. 

Comparing the numerous observations that have been 
made to ascertain the true obliquity, the mean of the 
several results gives about 50" in a century. " We 
may therefore state," says Professor Vince, " The 
secular diminution of the obliquity of the ecliptic, at 
this time, to be 50", as determined from the most ac- 
curate observations ; and this result agrees very well 
with that deduced from theory." 



o 


/ 


a 


23 


51 


20 


23 


51 


10 


23 


28 


24 


23 


28 






110 MAGNITUDES OF THE PLANETS. 

CHAPTER XLI. 

TO FIND THE PROPORTIONATE MAGNITUDES OF THE 

PLANETS. 

To find the proportion that any planet bears to the 
earth, or that one globe bears to another, the diameter 
of each must be cubed, and the greater number divided 
by the less : the quotient will show the proportion that 
one bears to another : for all spheres or globes are in 
proportion to one another as the cubes of their diame- 
ters. 

The cube of any number is the product of that number multiplied 
twice into itself. Thus, the cube of 2 is 8 ; for 2 multiplied by 2 makes 
4, and 4 multiplied again by 2 makes 8. — So the cube of 3 is 27 ; for 
3X3X3=27. 

If the diameter of the sun, as some assert, be 893,522 
miles : and of the earth 7,920 miles ; then the cube of 
893,522 is 713371492260872648, and of 7,920 is 
496793088000, and the greater number divided by the 
less will give 1435952, and so many times is the bulk 
of the sun greater than that of the earth. 

TO FIND THE PLANETS' DISTANCE FROM THE SUN. 

By the transits of Venus (already explained, page 
101,) the distance of the earth from the sun has been 
found to be about 95,000,000 of miles ; and by know- 
ing the earth's distance, the distances of the other pla 
nets are calculated. 

Kepler, a great astronomer, discovered that all the 
planets are subject to one general law, which is, that 
the squares of their periodical times are proportional 
to the cubes of their distances from the sun. And this 
law was fully demonstrated by Sir Isaac Newton. 



1 1 1 DISTANCES OF THE PLANETS. 

By their periodical times is meant the time they take in revolving 
round the sun : thus the periodical time of the earth is 365* days ; that 
of Venus, about 224£ days ; that of Mercury nearly 88 days. 

Therefore, if we would find the distance of Mercury 
from the sun, we say, as the square of 365 days is to 
the cube of 95,000,000, so is the square of 88 days to 
a fourth number, which will be the cube of its distance. 
And if the cube root of this number be extracted, the 
answer will be nearly 37,000,000 of miles 

Thus the square of 365=133225 j the cube of 95=857375; and the 
square of 88=7744. Therefore, as 133225 is to 857375, so is 7744 to 
49836, the cube of the mean distance of Mercury. And if the root of 
49836 be extracted, it will be more than 36£, =the mean distance of 
Mercury from the sun in millions of miles. 



QUESTIONS 

FOR EXAMINATION IN ASTRONOMY. 



Chapter I. 

What is Astronomy ? — Of how many parts does it consist, and what 
are they? — What does descriptive Astronomy treat of? — And what 
does physical ? — What is a circle ? 

What is the circumference sometimes termed ? 

What is the radius ? — What the diameter of a circle ? 

Name the proportion between the diameter and radius. 

What is an arc of a circle ? — What is a chord of a circle ? — Does a 
chord necessarily divide a circle into two unequal or equal parts ? — 
What is a semicircle ? 

By what other name is a semicircle sometimes called ? 

What is a quadrant ? 

What is the quarter of the periphery of a circle sometimes termed? 

Into how many parts are all circles supposed to be divided ? — How 
are degrees marked ? — How minutes and seconds ? — Mention the num- 
ber of degrees in a semicircle and in a quadrant. — What is an angle ? 
— Which is the angular point ? — Which are the legs of a right-angled 
triangle ? — What is a right angle ? — What is the measure of a right 
angle ? — What is an acute, what an obtuse angle ? — Define what are pa- 
rallel lines. — What is a globe or sphere ? — What is a spheroid ? — What 
is a great circle of a sphere 1 — What is a small circle of a sphere ? — 
What is the diameter of a sphere to any great circle termed ? — What are 
the extremities of the diameter called ? 

What distance is the pole of a great circle from every part of the dia- 
meter ? and for what reason ? — Into what parts, and whether equal or 
not, do two great circles divide each other ? and why ? 

What is the axis of the earth ? 



Chapter II. 

Fully define the science of Astronomy. 

What is the general opinion of Astronomers with respect to the dif- 
fereUsy stems of the universe ? 

L 113 



... 



114 QUESTIONS FOR EXAMINATION. 

What are the sun and moon termed ?— How are stars distinguished ? 
— Whence do the planets receive their light ? — What attendants have 
they ? — Is there any other order ? — What are the names of the planets, 
and which are the Asteroids ? — What are these called, and how many 
moons are there ? — To what planets do they belong ? 

The Sun. 

What is the Sun ? — What his form, diameter, and circumference ? 
What is the sun's diameter equal to ? 
What is his distance from the earth ; and how much larger ? 
What was the sun formerly thought to be ? 
What does Dr. Herschel suppose the sun to be ? 
What can be seen on the sun's surface ? 
What is meant by maculae and faculse ? 
What new opinion is formed respecting it ? 

How many motions has the sun, and what are they 1— What doe^the 
sun's motion about its axis render it ? 



Chapter III. — Mercury. 

Name the smallest and nearest planet to the sun ?— What is his dia- 
meter, and in what time does he revolve about the sun ? — At what dis- 
tance, and at what rate does he move in his orbit ? 

What proportion do the mean distances of Mercury and the earth from 
the sin bear to each other ? 

What appearance has Mercury ? 

How will the sun's diameter appear, if viewed from Mercury, and 
how much greater is the light and heat he receives than that of the 
earth ? 

In what manner does he change his phases ? 

How does this planet appear to us ? — How is it known that he does 
not shine by his own light ? 

When the orbit of this planet is between that of the earth and the 
sun, what is it denominated ? 

When did the last transit of this planet happen, and when will the 
next? 

Venus. 

What is the next nearest planet to the sun, and how is she distin- 
guished ? — What is her distance from the sun ? — In what time does she 
complete her annual revolution; and in what her rotation about her 1 
axis? 



QUESTIONS FOR EXAMINATION. 115 

What do astronomers make a complete rotation to be ? 

What is her magnitude ; what her diameter, and at what rate does 
she move in her orbit? — Is her quantity of light and heat greater than 
that of the earth ? — What is her appearance as seen by the naked eye ; 
and what, when viewed through a telescope ? — What is Venus deno- 
minated when seen by us westward of the sun ; and what when east- 
ward ? — Is there any difference in her seasons, and why ? 

Does she always appear of the same size, and what do her variations 
demonstrate ? 

Are there any transits of Venus, and how often do they occur ? 

When was the last seen, and when will the next happen ? — What 
have astronomers ascertained by this phenomena ? — Who was the first 
person that predicted the transit of Venus and Mercury ? — When was 
the first time Venus was ever seen upon the sun, and by whom? 



Chapter IV. — The Earth. 

Which is the third planet from the sun, what its mean distance, its 
diameter, and its circumference ? 

What would be the appearance of the Earth from the planet Venus ? 

What are the Earth's motions ? — At what rate does it move in its or- 
bit? — In what time does it perform an entire revolution, and what does 
a complete rotation form ? 

What is the more exact time of its annual motion ? — By what is time 
divided ? — On what does the former, and on what does the latter de- 
pend? 

What is the true form of the Earth ? 

What form was the Earth formerly supposed to be ? and what since 
proved to be I 

Of what service is the earth to the moon, and of what size does she 
appear, viewed from the moon ? 

The Mom. 

To what planet is the Moon a satellite ? — In what time does it re- 
volve in its orbit ?— What is the mean distance of the Moon from the 
earth, and at what rate does she move in her orbit ? — What is her dia- 
meter, and bulk ? — In what time is her rotation on her axis performed, 
and what the length of her day and night ? — How often does she re- 
volve round the earth in a year? — What is the length of her year ? — 
What are the phases of the Moon ? — Whence does the Moon receive 
her light ? — What enlightens that part of the Moon which is turned 



116 QUESTIONS FOR EXAMINATION. 

from the sun ? — Has the Moon any diversity of seasons ? — What do the 
shades which appear on the face of the Moon result from? 

What were the former opinions respecting the mountains of the 
Moon ? — What are the present ? — What else is observed in it i — When 
can the irregularity of the Moon's surface be most distinctly seen ? 

When is the Moon invisible to us ? and what is her first appearance 
called ? 

Which hemisphere of the Moon is never completely dark, and why ? 
— How long is the other hemisphere enlightened ? 

Is the moon thought to be inhabited ? — What is supposed concerning 
seas in the Moon, or her atmosphere ? 



Chapter V. — Mars. 

Which is the next planet to the earth, and how is he known in the 
heavens ? — What is his distance from the sun, and what the length of 
his year ? 

Has the cause of his dusky red colour been ascertained ? — At what 
rate does he move in his orbit ? — In what time is the diurnal motion of 
this planet performed ? — What is his diameter ? — What portion of light 
does he enjoy ? 

What is the mean distance of Mars from the sun, in regard to our 
earth ? How is the diurnal motion of Mars ascertained ? — Who first dis- 
covered them, and what has been since determined from them ? 

How does Mars appear when viewed through a telescope ? — Has he 
any satellites ? 

How does he appear when opposite the sun ? and what does it prove ? 
— Is the earth or sun in the centre of his motion ? 

Asteroids. 

Have any planets been discovered between the orbits of Mars and 
Jupiter ? — What are their names ? — Which is the nearest to Mars ? — 
What is its mean distance from the sun ? — How soon is its revolution 
through its orbit performed ? — How many degrees does it incline to the 
ecliptic ? 

By whom was Vesta discovered, and when ? 

What is the mean distance of Ceres from the sun ? — What its time of 
revolution, its diameter, and its inclination to the ecliptic ? 

By whom was Ceres discovered, and when ? 

What is the mean distance of Pallas from the sun ? — What is the time 






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QUESTIONS FOR EXAMINATION. 117 

of its revolution ? — What its diurnal motion ? — How great is its inclina- 
tion to the ecliptic ? — What is its diameter ? 

By whom was Pallas discovered, and when ? 

What is the mean distance of Juno from the sun, and what is its size ? 
— In what time is its revolution round the sun performed ? — What its 
diameter ?— What is the inclination of its axis to the ecliptic ? and what 
does it appear like ? 

By whom was it discovered ? 



Chapter VI. — Jupiter. 

Between what planets does the orbit of Jupiter lie ? — What his mag- 
nitude ? and how is he distinguished ? — What is the distance of Jupiter 
from the sun ? — What his mean distance from the sun ? — How much 
farther than the earth, and what proportion of light and heat does he 
receive? — What is the diameter of Jupiter, and how much larger is he 
than the earth ? — What proportion does his year bear to ours ? — In what 
time does he make his revolution round the sun, and at what rate does 
he move in his orbit? — In what time does Jupiter revolve on his axis? 
— Does his equatorial exceed his polar diameter ? — Does his axis incline 
to his orbit ? — What difference in his seasons ? and what variation in 
his days and nights ? — What is the length of his day and night ? — What 
appearance has he viewed through a telescope ? 

To what variations are his zones or belts subject, and what are they 
supposed to be? — Are they supposed to adhere to the body of the 
planet ? 

Jupiter's Satellites. 

How many satellites has this planet ? — In what time does the nearest 
make a revolution ? — What the most distant ? — By whom were they 
first discovered ? — What were they first taken to be ? — What are the 
periodical times of the first, second, third, and fourth ?— To what pur- 
pose have their eclipses been applied ? 



Chapter VII. — Saturn. 

What was Saturn formerly thought to be ?— What is his appearance ? 
—What his mean distance from the sun ? — What light and heat has 
he in proportion to the earth ? — What proportion does his light bear to 
that of our full moon ? — What is the diameter and magnitude of Sa- 
turn ? — In what time does he perform his revolution in his orbit ? — 

L 2 



118 QUESTIONS FOR EXAMINATION. 

How many miles does he travel in an hour ? — In what time does he 
revolve about his axis ? — Who ascertained it ? 

Satellites of Saturn. 

How many Satellites or moons is Saturn encompassed with ? — Of 
what use are they supposed to be ? — What distance is the nearest, and 
what is its breadth ? — Of what breadth is the outer ring ? — What is the 
space between them ? — What is it conjectured they are composed of? — 
In what time does the ring revolve about the planet ? 



Chapter VIII. — Uranus. 

Which is the most remote planet yet discovered ? — What appearance 
has he to the naked eye ? 

When can it be best perceived ? — Who discovered this planet, and 
when ? — Why is it named the Georgium Sidus ? — What is it called by- 
astronomers ? — What other names does it bear ? 

What is the distance of this planet from the sun? 

What is the distance given by some authors ? — What light and heat 
does he receive, compared with the earth ? 

In what time does he perform his annual revolution, and at what 
rate does he travel ? — What is his diameter ? 

The HersclieVs Satellites* 

How many Satellites has Herschel ? 

In what time does the nearest perform his revolution ? and in what 
the most remote ? 
Of what use are they supposed to be ? 

The Proportional Magnitude and Distance of Planets. 

How much larger is the Earth than Mercury, Venus, Mars, or Pal- 
las ?— How much larger than the Earth is Jupiter, Saturn, and Her- 
schel ? — How do astronomers express the mean distances of the planets ? 
—What distance from the sun may the different planets be estimated 
at ? — How are the distances calculated ? 



Chapter IX. — Comets. 

What are Comets thought to be ? and what direction do their orbits 
take? 
Are they supposed to be adapted to the habitation of animated be- 



QUESTIONS FOR EXAMINATION, 119 

ings ? — Whence is the name of Comet derived ? — What are their tails 
supposed to be ? — When could it happen thai the tail of a Comet could 
come near our atmosphere ? — Of how many Comets were the periods 
thought to be distinctly known I — When did the first appear I when 
the second ? and when the third I— What is the greatest distance of 
this Comet from the sun ? and what the least distance from the sun's 
centre I — At what rate does it travel \ 

How many miles in diameter was the head of the Comet of 1807 as- 
certained to be, and what that of 1811 ? — Of what nature are Comets ? 
— What did Sir Isaac j\ewton estimate the head of that Comet to be, 
seen by him in 1680 ? 

Whence are we authorized to conclude that Comets receive theii 
light \ 

Of what do comets consist ? — What is the nucleus, what the head, 
and what the coma ? — How long was the tail of the Comet of 1807 as- 
certained to be, and how long that of 1811 ? — What its distance from 
the sun, and what from the earth ? 



Chapter X. — The Fixed Stars. 

What are the heavenly bodies beyond our system called ? 

What is it probable they are ? 

By what light do the fixed stars shine ? 

How much nearer are we to some stars at one time, than at another. 

What is the distance of Sirius, or the Dog-star, from us ? — In what 
time would a cannon ball reach us from that star ? 

How much farther from us than the sun is the nearest fixed star ? — 
Have any been observed to revolve on their axis ? 

What is it probable the fixed stars are ? — Into how many magnitudes 
are they usually classed ? — What are the largest called ? — What the 
smallest ? — How r many are visible to the naked eye at one time ? 

What is the occasion of the stars appearing to us innumerable ? 

Do not some of the fixed stars, w T hen viewed through a telescope, 
appear double or treble ? — What are clusters of stars called ? — Which is 
the most remarkable of the clusters called nebulae ? — What has Dr. 
Herschel remarked concerning the Milky Way ? 

What is observed of the Magellanic clouds ? — Have not a greater 
number of stars been observed since the use of telescopes ? 

How are planets distinguished from fixed stars ? 



120 QUESTIONS FOR EXAMINATION. 

What is thought to occasion the twinkling of the fixed stars ? 

Are all stars that were known to the ancients, now to be seen ? — 
And are not some now seen that were not noticed by them ? 

By whom is the most ancient observation of a new star ? — Which 
the first we have any accurate account of? 

Have not some stars alternately appeared and disappeared ? What 
have other stars been subject to ? 

What star was discovered in 1600 ? — What were its different appear- 
ances ? — What was discovered respecting /3 Lyrae ? 

What appearance has the heavens to a spectator in any part of the 
universe ? — What proof have we of this ? — If transplanted to a planet 
belonging to Sirius, how would that star and our sun appear to us? 

What is the vulgar error respecting the stars ? 



Chapter XL — Constellations. 

Into what did the ancients form the stars? 

For what purpose were the constellations formed ? 

What was the ancient, and what the present number of the constel- 
lations ? — By what are the heavens usually distinguished ? — What is 
the number of the constellations in the northern hemisphere ? — What 
in the southern ? and what in the zodiac ? — What are the stars called 
not comprehended in these. — Name the northern constellations, and 
the southern. — Repeat the zodiacal constellations. How are some par- 
ticular stars distinguished ?— How are others denoted ? 



Chapter XII. — Different Systems. 

What is the system called which has been described ? — By whom 
was it formerly taught ? — By whom revived ? — What did Ptolemy sup- 
pose? 

What are epicycloids ? 

What system did the Egyptians receive ? — Who at length adopted 
the Pythagorean ? — How did Copernicus place the sun and planets ? — 
What system did Tycho Brahe endeavour to establish ? — By whom was 
the solar system first taught? — By whom revived ?-~By whom con- 
firmed ? — And who at length fully established it ? 



QUESTIONS FOR EXAMINATION. 121 

Chapter XIII. — On the Motions of the Planets. 

How would the planets appear to move if seen from the sun ? — How 
do they appear to move as seen from the earth ? 

Give some illustration of the motions of the planets. 

When is their motion direct ? — When retrograde ? — When sta- 
tionary ? 

Inferior and Superior Conjunctions of the Planets. 

What is a planet in its inferior conjunction?— When in its superior T 
— What planets have alternately a conjunction and an opposition ? — 
And when ? — In which case do they rise and set nearly with the sun ? 
— When is it the reverse ? — Does the appearance of a planet vary if 
view T ed through a telescope ? — When is Venus seen with nearly a full 
face ? — When only half enlightened ? 

When can Mercury and Venus be seen in their inferior conjunction t 

What planets do these appearances refer to I 



Chapter XIV, — The Plane of an Orbit, Planets f 

Nodes, fyc+ 

What circle does the earth describe as seen from the sun ? 

In what different signs do the earth and sun appear ? 

What is understood by the plane of a circle ? 

Give some illustration. 

In what do the orbit of the earth and the ecliptic vary ? 

Give some illustration. 

Do the orbits of the planets vary from the ecliptic ? — What is meant 
by the obliquity of their orbits ? — Demonstrate it by the figure. — What 
is meant by the line of the nodes ? — What by the ascending, and what 
by the descending node ? — What is really meant by the terms plane 
and orbit 2 

Transits of Mercury and Venus. 

Define by plate VIII. fig. 1, and by plate XIV. fig. 6, the transits of 
Venus or Mercury. — Are there great variations in the magnitude of 
Venus, as seen from the earth ? — Demonstrate this by the figure, plate* 
VII. fig. 1. — What is the least distance of Venus from the earth? — 
What the greatest ? 

Explain the phases of Venus, in her orbit, by the figure. 



122 QUESTIONS FOR EXAMINATION. 

Chapter XV. — The Ecliptic, Zodiac, Equator, dfc. 

What is the ecliptic ? — Name the most conspicuous stars near the 
ecliptic. 

From what stars is the moon's distance calculated ? — Why is the 
ecliptic so called ? 

Whence arises the obliquity of the ecliptic ? — What are the points of 
intersection called ? — What are the times of intersection called ? — What 
is the zodiac ? 

Whence is the term zodiac derived ? 

Give the names and characters of the twelve signs ? — Which are the 
northern signs? — Which the southern? — Which are called the as- 
cending ? — Which, descending ? — To what do the signs correspond ? — 
How much of the ecliptic does the earth pass over each day ? — How 
much each month ? — How many degrees in a sign ? — And why ? — 
What is the terrestrial equator ? — What is its distance from the poles ? 
— How does it separate the globe ? — What is the celestial equator ? 

Of the Ephemeris. 

What does the first column of the Ephemeris show ? — What the sec- 
ond ?— What the third ? 

If you know the time of the sun's rising, how do you know the time 
of its setting, and vice versa ? 

What does the fourth column show ? 

What and when is the sun's greatest declination? —When will he 
have no declination ? — What is meant by declination ? 

When does an astronomical day begin ? — What do the three next 
columns contain ? — What is meant by southing ? — How often and when 
does the moon come to the meridian with the sun ? 

How much later, one day with another, does the moon culminate ? 

What does the eighth column show ? — What is the adjusting of time 
called ? 

How often and at what times are the clock and dials together ? 

How are the clocks, &c. regulated ? — What does the first short col- 
umn ? — What the second short column ? — What the five following col- 
umns ? — What is meant by the heliocentric longitude ? — And what by 
the geocentric^ 

Define the heliocentric and geocentric longitudes by the figure. — 
Which longitude is given in page 9 of the Ephemeris ? 

Explain the column for daylight, — What is meant by the latitude 
of a planet ? — And what columns show the latitude ? — How is the Ion- 



QUESTIONS FOR EXAMINATION. 123 

gitude of a heavenly body usually expressed ? — Which of the columns 
speak of the rising or setting of a planet I — Why not of both ? 



Chapter XVI. 

What is a degree ? — What is the measure of an angle ? 

Explain this by fig. 3, plate IX. 

What are the poles ? — What parts of the heavens appear motionless? 
—And what part appears to have the greatest motion ? — What are the 
tropics ? — What their distances from the equator ? — What are the polar 
circles ? — What their distance from the poles ? 

Why is the distance of the polar circles fixed at that number of de- 
grees from the poles ? 

Why are the meridians so called ? — How many meridians are 
usually drawn on the globes, and why ? — Are these ail that can be re- 
presented ? 

Explain this by fig. 3, plate IX. 

What is meant by longitude ? — Through what place does the first 
meridian pass? — How many degrees are equal to an hour? — What 
places are before London, in time, and what after? — How do you re- 
duce longitude to time ? 

Give the reason why 15 degrees are equal to an hour ; and 30 de- 
grees to two hours, &c. — If 12 o'clock at London, what are the times at 
Barbadoes, at St. Petersburgh, and at Calcutta. 

How is time turned into longitude ? — What is meant by the latitude 
of a place ? — What by the latitude of a heavenly body? — What are the 
colures ? — How many zones are there, and what are they ? — What are 
the solstitial points ? And why so called ? — What are the equinoctial 
points ? And why so called ? 



Chapter XVII. — Planets' orbits Elliptical. 

What are the orbits of the planets termed ? — Illustrate this by figures 
2, 3, and 5, of plate VIII. — WTien is a planet said to be in its perihelion, 
and when in its aphelion ? — And when at its middle or mean distance ? 
— What is termed the eccentricity of its orbit ? 

Attraction of Gravitation. 

What is meant by attraction ? 

What is attraction of magnetism ? — What attraction of electricity ? — 
What of cohesion ? 



124 QUESTIONS FOR EXAMINATION. 

What is attraction of gravitation ? In what proportion is this attrac- 
tion ? — By what kind of attraction does the sun affect the earth, and the 
earth the moon ? 

Upon what principle does the stone fall to the earth — and the waters 
of the ocean gravitate, &c 

Repeat one of the laws of attraction. — Illustrate this by the figures 4 
and 5 of plate X. — What is the second law of gravity ? — Do equal mag- 
nitudes imply equal quantities of matter ? — With what proportion does 
the sun attract the earth ? And why ? — Explain this otherwise, by boats 
of equal bulk. 



Chapter XVIII. — Of Attractive and Projectile 

Forces* 

What power counteracts that of attraction ? — What would be the ef- 
fect of rectilineal motion ? — Of what are the planets' motions com- 
pounded ? 

Explain this by some projectile force. — What, if a ball be thrown from 
the hand ? 

What united forces retain the planets in their orbits ? 

Explain the difference of a circular motion and a straight line. — Give 
a further explanation by the figure 4, plate VIII. 

What results from the two forces being equal ? 

What would result if either power were to cease acting ? 

By what laws are the secondaiy planets governed ? — Why are the 
planets' orbits not true circles ? 

Explain by the figure, what is meant by equal portions in equal times. 
— And by unequal portions in equal times. 

What power will a double velocity balance ?— Demonstrate this by 
the figure. — What is meant by equal areas in equal times ? — What re 
suits from the comets' orbits being so very elliptical ? 

Suppose a body to receive two different impulses, what would be it* 
direction ? — Epxlain this by the figure. 



Chapter XIX. — The Centre of Gravity. 

What is the centre of gravity ? — Explain this by figure 6, plate X. 
If the earth were the only attendant on the sun, what motion would 
the sun have ? 
What, if all the planets were on the same side of him ? — Are the se- 



QUESTIONS FOR EXAMINATION. 125 

condaries governed by the same laws ? — What is supposed of every 
system in the universe ? 

The Horizon. 

What is the horizon ? — To what does the rational horizon apply ? — 
Explain this by fig. 2, plate IV. 

How is this horizon represented on the artificial globe ? 

What does the sensible horizon respect ? — How is its extent varied ? 

Refer to the figure. — What is the extent of view, to an eye elevated 
five feet ? And to one elevated twenty feet ? — How T do you mark the 
difference of the two horizons ? 

Why do persons on the sensible horizon see the heavenly bodies when 
on the rational ? 

What proportion does the earth's semi-diameter bear to the sun's dis- 
tance ? — And what is the result? — What proportion does the earth's 
semi -diameter bear to the moon's distance. 



Chapter XX. — Day and Night. 

What is the cause of the succession of day and night ? — Illustrate 
this by fig. 2, plate IV. — How much of a sphere does the sun illumine 
at one time ? — How much of the heavens can a spectator behold at one 
time ? 

Explain the apparent motion of the heavenly bodies, by some fami- 
liar motions on our earth. 

How are the apparent motions of the whole starry firmament ac- 
counted for ? 

What results from the earth's motion to persons in the latitude of 
London? — What, to those on the equator? 

What points in the heavens keep the same positions ? — Why are stars 
not seen by day ? — How many revolutions on its axis does the earth 
make in a year ? — Why are w T e not sensible of the earth's daily motion ? 

What proof have we of other motion not being perceptible ? 



Chapter. XXI. — The Atmosphere. 

What is the atmosphere ? — What does it possess ? — Where is it most 
dense ? And where more rare ? 
What does the whole mass of atmosphere contain ? 

M 



126 QUESTIONS FOR EXAMINATION. 

To what purposes does it serve ? — Of what appearances is it the cause ? 

What do experiments on the air-pump prove ? 

Without an atmosphere how would the sky appear? — To what height 
does the atmosphere extend ? — At what height does it cease to reflect 
the rays of light ? — What results from the sun's rays falling upon the 
atmosphere before he rises ? And after he sets ? 

When does twilight >begin? — When does it end? 



Chapter XXII. — Refraction. 

When do the rays of light deviate from a rectilineal course ? — From 
this cause ^hat results ? — What is the apparent elevation called ? 

Demonstrate this by fig. 1, plate XL 

What is the consequence of this refraction ? — How much longer does 
the sun appear by this refraction ?— Explain this by the figure. 

How can you show the effects of refraction ? — Have you not another 
way of demonstrating it ? 



Chapter XXIII. — Parallax. 

What is the parallax of the sun or moon ? 

Which is called its apparent, and which its true place ? 

When is the parallax the greatest ? — And what is that parallax called ? 

What is the sun's mean parallax ? Why seldom made use of? And 
for what purpose ? — Have the fixed stars any parallax ? 

Does the parallax of the sun or moon depress or elevate them ? How 
must their true altitudes be obtained ? — Illustrate this by fig. 2, plate 
XI — Does distance cause the parallax to be greater or less ? — Where 
has any object its greatest and where its least parallax ? — When is the 
parallax nothing ? — Explain this by the figure. 



Chapter XXIV. — Equation of Time. 

How much longer is the summer than the winter half year ? — By 
what occasioned ? — Of what is this inequality the cause ? — What keeps 
true time ? — And what apparent time ? — What is the difference of these 
termed? 

Equal time, how measured ? — and apparent time, how? 

Upon what does this difference depend ? — What motion is the most 



QUESTIONS FOR EXAMINATION. 127 

equable in nature ?— In what time is the earth's rotation completed ? — 
What is this space 1 called I And why ? 

If the earth had only a diurnal motion, what would be the length of 
fee day f 

What is a solar or natural day? — By what is this difference oc- 
casioned | 

Will the hands of a clock convey any idea of this? 

How often are the ecliptic and zodiac coincident? — And when? — 
Why do they differ at other times? 

Explain this by the globe. — Refer also to figured — What do the 
marks on the ecliptic represent? — 'And what those on the equator? 

In what quarters will the sun be faster, and in whatsZoiuer than the 
clockfl I And why? — Will not the elliptic form of the earth's orbit oc- 
casion a variation ? 

What, if the differences depended solely on the inclination of the 
earth's axis .' — Refer to an Kphcmeris for the times of the clock and 
dials coinciding, and say on what days. 

If the earth's motions in its orbit were uniform, what would result ? — 
What is the earth's daily course in winter, what in summer? — From 
this cause, what variations are there in the natural day? And why ?— 
What then are the combined causes of the inequalities of time? 



CiiAFrER XXV. — The Seasons. 

What Ls the inclination of the axis of the earth ? — Explain this by the 
olate. — What is ohsorved of the axis of the earth? 

Illustrate the earth's parallelism. 

What is the diameter of the earth's orbit? — To What does the axis of 
die earth always point, and how do you account for it? 

Can you illustrate this by something familiar? 

What proof is deduced from this? 

How is the earth's course round the sun proved ? 

('an these observations be made in the day? 

Upon what docs the variety of the seasons depend? — What, if the 
axis of the earth were, as in the figure, perpendicular to the sun'srays? 

Why must the poles be excepted ? 

What would result from such a position! 

On what does the proportion of heat materially depend ? 

Explain it by the figure. 

Represent by figure 2, plate X, the position of the earth in our sum- 
mer season. 



128 QUESTIONS FOR EXAMINATION. 

What is evident from the circle in the latitude of London ? — What is 
then the appearance at each pole ? 

What is observed of places in equal latitudes, the one north, the other 
south ? 



Chapter XXVI. — Seasons, continued. 

What is represented by fig. 2, plate XII. ? 

How much nearer are we to the sun in December than in June ? — 
What is the sun's apparent diameter in winter ? — What in summer ? 

What is the time we denominate our summer ? — How much longer 
than our winter half-year ? — What inference is consequent ? 

Whence does the coldness of our winters arise ? — When are the hot- 
test and when the coldest seasons ? 

In June, what pole inclines to the sun ? And what results there- 
from? — In December what pole inclines to the sun? And where is it 
then winter ? — In March and September what position has the axis ? — 
What length are the days and nights ? 

In March, what is the real place of the earth? — In what sign will the 
sun then appear ? — On the 21st of June, where is the sun vertical ? — 
Where in September ? — Where in December ? 

What causes produce the increase and decrease of days and nights? 
— To what parts is the sun vertical, from 20th March to 21st June ? — 
And from June to September? 

To what parts is the sun vertical from 23d September to 21st De- 
cember? — And from December to March? — How often is the sun ver- 
tical to every part, between the tropics ? 



Chapter XXVII. — The Moon's Months, Phases. 

What kind of months are they ? — And what is the length of each ?— 
Whence arises the difference ? 

Explain this by the figure. — Is the moon's orbit a circle, or an el- 
lipsis ? 

How much of the moon is at one time enlightened ? — Do we always 
see the whole enlightened side ? 

Refer again to the figure. 

What is the moon's position at change ? — What, at full moon? — What, 
when changed ? And what is the moon then said to be in ? — What, 
when three-fourths are seen ? — What, when wholly enlightened ? 



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(,-'/ 

*^-^ 


— ^s 



7 



QUESTIONS FOR EXAMINATION. 129 

In what directions are the liorns just after the change ? — What, after 
the full moon ? — Represent the moon's phases by a ball, or small globe. 
What is the moon's apparent motion ? — What, the real motion ? 
By what may the moon's real motion be known ? 



Chapter XXVITI. — Eclipses — First, of the Moon. 

What does the term eclipse imply ? — By what is an eclipse of the 
moon occasioned ? — When must an eclipse of the moon happen? — Re- 
fer to the plate. — What would result if the moon's orbit coincided with 
the ecliptic ? 

How much does the orbit of the moon vary from the ecliptic ? 

What is the greatest distance from the node, at which an eclipse of 
the moon can happen ? — When an eclipse happens full in the node, 
what is it called ? — What is the duration of an eclipse ? — Of what shape 
is the earth's shadow 7 ? — Does not the moon's distance from the earth 
vary ? 

How does the moon's being either nearer or more distant, affect the 
length of an eclipse ? 

On which side of the moon does an eclipse begin, and on which side 
end ? 

How may this be clearly conceived ? 

How are eclipses calculated ? 

Of what form is the earth's shadow ? — What does that demonstrate ? 
— How is the sun proved to be larger than the earth ? — If the two bodies 
were equal, of what shape would be the shadow ? — And if the earth 
were the larger body, of what shape would be the shadow ? 

Eclipse of the Sun. 

When does an eclipse of the sun happen ? — Explain it by the figure. 

Illustrate it by a suspended ball or globe. 

If the whole of the sun be obscured, what is the eclipse termed ? — 
What, if only a part ? 

What does the word digit mean ? 

When, only, can the moon cover the sun's whole disc? — Within how 
many degrees of the node can an eclipse happen? — At all other new 
moons, how does she pass? — And how at all other full moons ? — If an 
eclipse of the moon be central, what results? — And what, if an eclipse 
of the sun be central ? — What are annular eclipses ? — By what occa- 
sioned ? — When only can an eclipse of the sun be total ? — How long 

M 2 



130 QUESTIONS FOR EXAMINATION. 

may total darkness last ? — How many solar eclipses in a year must 
there be ? — What is the least number there may be ? — What is the least, 
and what the greatest number of lunar eclipses ? — How many eclipses 
may happen in a year? — In this case, how many of each ? — What is the 
mean number of eclipses? — Why are there more solar than lunar 
eclipses? — And in what proportion?— Why, then, are more lunar than 
solar eclipses seen ? 



Chapter XXIX. — Polar Day and Night. 

How are the long days and nights around the poles accounted for ? — 
How, when the sun is on the equator ? — How, when vertical to the 
tropic of Cancer ? — What is the extent of the sun's rays ? — What the 
length of each day and night? — And why ? 

What benefit have the polar regions from the twilight ? — How long 
does the moon continue in their horizon ? — Explain the reason. — What 
third benefit do they receive ? — How does the moon's track vary from 
the sun's course ? 

When the sun is in the equator, in what point does he rise? — How, 
during the summer half-year? — How during the winter half-year? 

Whence arises a small variation between the rising and setting? — 
Explain this by the globe. 



Chapter XXX. — Umbra and Penumbra. 

Explain the meaning of Umbra and Penumbra by the figure ? Which 
parts will suffer a total eclipse, and which a partial ? — How does the 
umbra fall in an annular eclipse? — And what will then be its appear- 
ance ? — Which parts of the earth will have a partial eclipse? — And to 
what parts no eclipse. 

How long can the annular appearance remain ? — What is the moon's 
mean motion ? — How many miles does it answer to ? — What will be 
the relative velocity of the moon's shadow ? — What affects the length 
of a solar eclipse ? 

Explain the different eclipses by the figure, in the 1st, 2d, and 3d po- 
sitions. 

What were the effects of a total eclipse of the sun according to Cap- 
tain Stannyan ? — What is Dr. Scheuchzer's account ? — Relate Dr. Hal- 
ley's description. 



QUESTIONS FOR EXAMINATION. 131 



Chapter XXXI. — Transits of Venus. 

Illustrate a transit of Venus, by the figure. — During which conjunc- 
tion does the transit take place I — What is the principal use to which 
astronomers apply the transits of Venus ? 

To what other purposes are the transits applied ? — Which take place 
the oftener, the transits of Mercury or Venus ? — And which are of the 
greater utility ? 

What is meant by the occultation of the fixed stars ? — By what me- 
thods are occupations ascertained ? — What has Cassini remarked with 
respect to them ? 

What is meant by conjunction ? — What by latitude ? 

What computations are needful to determine when an occultation 
will happen ? 

Will the appearance be different at different places upon the earth ? — 
From what cause will the difference result ? — To what extent may the 
moon's parallax affect the obscuration ? 



Chapter XXXII. — The Harvest Moon. 

How much later does the moon often rise, one day than another ?— 
Is there any difference in different latitudes ? — What is her difference 
in rising about the time of harvest? 

What is the difference to those w T ho live in the latitude of London? 

How does the autumnal full moon rise in considerable latitudes ? — 
Why called the Harvest Moon ? 

By whom were these first observed ? — And to what ascribed ? — At 
what intervals of time does the moon rise about the equator ? — When, 
at the polar circles ? — How long does the moon shine within the polar 
circles without setting? — To what are these phenomena owing? — 
What is remarked of the signs Pisces and Aries ? — What difference is 
there in the moon's rising when in these signs ? — How do those signs 
of the ecliptic set, which rise with the smallest angles ? 

Illustrate this by the figure — demonstrate it by the globe. 

What part of the ecliptic makes the smallest angles, in northern lati- 
tudes ? — What, the greatest ? — What angle is made by Pisces and Aries 
when rising ? — What angle, when setting ? — What is the moon's differ- 
ence of rising when in Libra ? 

Demonstrate these phenomena on the globe. 



132 QUESTIONS FOR EXAMINATION. 

Why is the moon at the full when in Pisces and Aries only in our 
autumnal months? — What are the two autumnal full moons called? 



Chapter XXXIII. — Harvest Moon continued. 

How often does it happen that the moon rises, for a week together, 
so nearly in point of time ? 

What time of the day do Pisces and Aries rise in winter ? — And what 
is then the moon's age ? — How do these signs rise in spring ? — And 
what then the moon's age ? — When do Pisces and Aries rise in summer? 
— What is then the moon's age ? — Why is her rising then so unob- 
served ? 

In what time does the moon go through the ecliptic ? — What is the 
time from change to change? — What results therefrom? 

If the earth had no annual motion, how T would every new and full 
moon fall ? — And why? — How many degrees does the earth move du- 
ring one lunation? — How does this affect the moon's conjunction, &c. ? 
— If in any conjunction she were in at the first degree of Aries, w here 
would her next conjunction be ? — Why is the moon twice in some one 
degree every lunation ? 

How must the north and south poles appear to the inhabitants on the 
equator ? — What angle docs the ecliptic make to such ? — And what re- 
sults therefrom ? — Why have they no Harvest Moon at the equator ? — 
What effect has distance from the equator upon the rising of Pisces and 
Aries? 

Illustrate this by the globe. 

In what signs do the autumnal full moons happen to those in southern 
latitudes ? — With what angles do Virgo and Libra rise ? — What, with 
respect to harvest moons in southern latitudes ? 

What circumstance may cause some small difference in the time of 
the moon's rising or setting ? — How much does the moon, at times, vary 
from the ecliptic ? 

To what part of the earth does the full moon not rise in summer ?— 
To what part does she not set in winter ? — Explain the cause of this 
satisfactorily. 



Chapter XXXIV. — Leap Year. 

What is the time we call a year ? — What has been the usual division ? 
What were the ancient Hebrew months ? — What the extent of their 



QUESTIONS FOR EXAMINATION. 133 

year? — Of how many days did the Athenian months consist? and by 
whom regulated ? — How did Meton attempt to reconcile the difference? 
— How many months composed the year in the time of Romulus? — 
What addition was made to them by Numa Pompilius ? — What was the 
length of the Egyptian year? 

Who first attained to tolerable accuracy ? — How did Julius Caesar 
regulate the months ? — How allow for the six odd hours ? — What was 
every fourth year denominated ? — And what is it now called ? 

What day did the Romans reckon twice ? — And what was such in- 
tercalary day called ? — What day do we now add in leap-year ? 

How is it ascertained what years are, and what are not leap-years ? — 
Mention what year will and what will not be leap-years. — What is the 
length of the true solar year ? — How much docs 365 days 6 hours ex- 
ceed the true solar year ? — In how many years does it amount to a 
whole day ? — How long did the Julian year continue in use ? — Who 
reformed the calendar ? And how ? — How denominated ? — In what year 
did w T e adopt the new style into our calendars ? — And by what change 
m the days ? — Why were the years 1800 and 1900 computed as com- 
mon years ? — And why, every four hundredth year afterwards ? 

What will result from this method of reckoning ? 

From what day was the beginning of the year changed ? — How, for 
a time, did it affect the dates ? 



Chafper XXXV.— The Tides. 

Describe the fluctuations of the ocean. 

What were the ancients' ideas of the tides ? — Who made some suc- 
cessful advances ? — And who clearly pointed out the cause ? 

What is the true cause of the flowing of the tides ? 

How is the moon proved to be the cause of the tides ? 

What would be the appearance, if there were no influence from the 
sun or moon ? — What, if the earth and moon were without motion? — 
What proportion does the sun's attraction bear to that of the moon? — 
When the moon is at change, how many parts are raised 1 — If it be high 
water at A, fig. 4, plate XVI. what effect will it produce at C and D ? 

What is the attractive power of the sun and moon according to some 
authorities ? 

Explain the cause of low water at C and D. 

Of what form will the waters partake at full and change ? 



134 QUESTIONS FOR EXAMINATION. 



Chapter XXXVI. — The Tides, continued. 

In what proportion does the power of gravity diminish? — When 
there is a tide, as at A, fig. 4, plate XVI. what occasions a similar tide 
at B ? — From what cause will two tides be produced each day ? 

How has it been otherwise explained ? 

How often does the tide ebb and flow in twenty-four hours ? — What 
is the interval between the flux and reflux ? — What is the daily varia- 
tion as to the time of high water ? 

Give an example or two. 

How are the tides affected at the/wZZ of the moon ? — Explain this by 
fig. 6, plate XVI. 

If there were no moon, how would the sun affect the tides ? — When 
do the highest tides happen ? — What are such tides called ?— When the 
moon is in her quarters, what are the influences of the sun and moon ? 
— What are such tides called ? 



Chapter XXXVII. — The Tides, continued. 

Why are the tides higher at some seasons than at others ? — How long 
is it, in open seas, after the moon passes the meridian, that the tides are 
at the highest ? — And why ? 

Illustrate this by an impulse given to a moving ball — and by the 
time of the greatest heat of the day — and by the increasing heat in July 
and August. 

Why do not the tides always answer to the moon's distance from the 
meridian ? — When will the greatest spring-tide happen? And why ? — 
Why do the tides rise higher in channels and rivers ? 

To w r hat may the tides, in the mouths of rivers, be compared ? 

What retards the tides in shoals and channels ? — And how much are 
they retarded ? 

How long does the tide take to come to London bridge ? 

Have lakes any tides ? — What seas have but small elevations ? — 
Give me the reason. 

Are there tides in the air ? 

How long after the new and full moons do the greatest spring-tides 
happen ? — And how long after the first and third quarters do the least 
neap-tides happen ? — Are the tides unequal at places remote from the 
equator ? Where is this inequality observed ? — What has been remarked 
of the morning and the evening tides ? 



QUESTIONS FOR EXAMINATION. 135 

What results, when the moon's greatest elevation points to one side 
of the equator ? 

When and where is the inequality the greatest ? — What is observed 
of the moon when she has declination ? 



Chapter XXXVITI. — The Precession of the Equinox. 

What results from the earth's motion on its axis ? — What arises from 
the attraction of the sun and moon ? — If the sun sets out from any star, 
in what time will he relurn to it ? — And why? 

How do you prove that 20 minutes, 17i seconds of time are equal to 
50" of a degree ? — What is the sun's apparent annual motion ? 

When does the sun finish the tropical year ? — And what does a tro- 
pical year contain ? — When does he complete his sidereal year? — And 
what does it contain ? — How much longer is the sidereal year than the 
solar or tropical ? — And than the Julian or civil year ? 

Axe the lengths of the sidereal and solar years the same as given by 
another author? 

What is the sun's daily mean rate in a tropical year ? — When will he 
arrive at the same equinox? — How long will the sun and equinoctial 
points be in falling back 30° ? — What will be the apparent effect upon 
the fixed stars ? 

How do you prove that 50" short in one year, are equal to a whole 
sign in 2160 years ?— Explain it by fig..l, plate XVII. 

What results from the shifting of the equinoctial points? — What 
change has taken place since the infancy of astronomy ? 

How is the motion of the equinoctial points, or the precession of the 
equinoxes, found? — Who first observed this motion? — And by what 
means ? — With whom did Hipparchus compare his observations ? 

How many years is the equinox in shifting a whole degree ? — How 
long for a whole sign ? — What number of years completes the grand 
celestial period ? 

How much have the equinoctial points receded since the creation ? 



Chapters XXXIX and XL. — Precession oftheEqiil 
nox, continued. 

Explain the phenomena by fig. 3, plate XVII. 

How do astronomers determine the obliquity of the ecliptic? 



1J30 UUESTIONS FOR EXAMINATION. 

What did Eratosthenes, Ptolemy, Copernicus, and M. De la Lande 
find the obliquity to be ? — From these observations what is deduced ? 

What is the secular diminution of the ecliptic at this time? 

Give a full illustration of the precession of the equinox by the four 
small spheres, plate XVII. — What does the sphere marked 1 exhibit ? — 
What, the sphere 2 ? — What, the sphere 3 ? — What, the sphere 4? 



Chapter XLI. — Proportionate Magnitudes of the 
Planets. 

How is the proportion that one planet bears to another found ? — Re- 
peat the general law, All spheres, tyc. 

What is the cube of any number ? — Demonstrate this by the cubes of 
2 and 3. 

Cube the numbers 893522, and 7920. — Divide the greater by the less. 

To find the Planets' Distances from the Sun. 

How is the earth's distance from the sun found ? — What is its dis- 
tance ? — What other calculations can be made from it? — What general 
law did Kepler discover? — By whom was this law fully demonstrated? 

What is meant by their periodical times ? — Give instances of two or 
three. 

How do we find the distance of Mercury from the sun ? — Square 
365.— Cube 95,000,000.— Square 88.— State the question, and perform 
the operation. 



NEW TREATISE 



ON THE 



USE OF THE GLOBES; 



DESIGNED FOR 



THE INSTRUCTION OF YOUTH. 



ABRIDGED FROM THE LARGER WORK OP 

THOMAS KEITH. 



HutetetJ according to the glct of <£o\lQKZ3S in the year 1832, 
by Key & Mielke, in the Clerk's Office of the District Court of 
the Eastern District of Pennsylvania. 



ADVERTISEMENT. 

The present Abridgement of Keith on the Globes, has 
been prepared in order to meet a demand which has fre- 
quently been made by those teachers who are desirous to 
give their pupils a thorough course of Problems on the 
Globes, and who are, nevertheless, of opinion, that the larger 
work of Keith contains a great deal more than is necessary 
for this purpose. It is intended as a companion for Guy's 
Astronomy, a popular treatise, issuing simultaneously from 
the same press. It comprises, 

I. The extensive and clear definitions of Keith, including 
every thing which is necessary for a thorough knowledge 
of the structure, design, and uses of the globes. 

II. Nearly all Keith's Problems ; none being omitted 
which are of any practical utility for the general student. 

The portions of Keith's larger work, which have been 
omitted, belong properly to a treatise of Astronomy, and are 
superseded by the treatise which this abridgment is intended 
to accompany. 

3 



CONTENTS. 

CHAPTER I. 
Lines on the Artificial Globes, Astronomical Definitions, &c> . 5 

CHAPTER II. 
Problems performed with the Terrestrial Globe 24 

CHAPTER in. 
Problems performed with the Celestial Globe 128 



A 

NEW TREATISE 

ON 

THE USE OF THE GLOBES- 



CHAPTER L 

Explanation of the lines on the Artificial Globes, in- 
cluding Geographical and Astronomical Definitions , 
with a few Geographical Theorems* 

1. The Terrestrial Globe is an artificial repre- 
sentation of the earth. On this globe the four quar- 
ters of the world, the different empires, kingdoms and 
countries ; the chief cities, seas, rivers, &c. are truly 
represented, according to their relative situation on the 
real globe of the earth. The diurnal motion of this 
globe is from west to east. 

2. The Celestial Globe is an artificial represen- 
tation of the heavens, on which the stars are laid down 
in their natural situations. The diurnal motion of 
this globe is from east to west, and represents the ap- 
parent diurnal motion of the sun, moon and stars. In 
using this globe, the student is supposed to be situated 
in the centre of it, and viewing the stars in the con- 
cave surface. 

a 2 n 2 5 



6 DEFINITIONS, &C. 

3. The Axis of the Earth is an imaginary line 
passing through the centre of it, upon which it is sup- 
posed to turn, and about which all the heavenly bodies 
appear to have a diurnal revolution. This line is rep- 
resented by the wire which passes from north to south, 
through the middle of the artificial globe. 

4. The Poles of the Earth are the two extremities 
of the axis, where it is supposed to cut the surface of 
the earth, one of which is called the north, or arctic 
pole ; the other the south or antarctic pole. The ce- 
lestial poles are two imaginary points in the heavens, 
exactly above the terrestrial poles. 

5. The Brazen Meridian is the circle in which 
the artificial globe turns, and is divided into 360 equal 
parts, called degrees. In the upper semicircle of the 
brass meridian these degrees are numbered from to 
90, from the equator towards the poles, and are used 
for finding the latitudes of places. On the lower semi- 
circle of the brass meridian they are numbered from 
to 90 ; from the poles towards the equator, and are 
used in the elevation of the poles. 

6. Great Circles divide the globe into two equal 
parts, as the equator, ecliptic, and the colures. 

7. Small Circles divide the globe into two unequal 
parts, as the tropics, polar circles, parallels of latitude, 
&c. 

8. Meridians, or Lines of Longitude, are semicir- 
cles, extending from the north to the south pole, and 
cutting the equator at right angles. Every place upon 
the globe is supposed to have a meridian passing through 
it, though there be only 24 drawn upon the terrestrial 



DEFINITIONS, &C. 7 

globe ; the deficiency is supplied by the brass meri- 
dian. When the sun comes to the meridian of any 
place (not within the polar circles,) it is noon or mid- 
day at that place. 

9. The First Meridian is that from which geogra- 
phers begin to count the longitudes of places. In Eng- 
lish maps and globes the first meridian is a semicircle 
supposed to pass through London, or the royal obser- 
vatory at Greenwich. 

10. The Equator is a great circle of the earth, equi- 
distant from the poles, and divides the globe into two 
hemispheres, northern and southern. The latitudes of 
places are counted from the equator, northward and 
southward, and the longitude of places are reckoned 
upon it, eastward and westward. 

The equator, when referred to the heavens, is called 
the equinoctial; because when the sun appears in it, 
the days and nights are equal all over the world, viz. 
12 hours each. The declinations of the sun, stars and 
planets, are counted from the equinoctial northward 
and southward, and their right ascensions are reckoned 
upon it eastward round the celestial globe from to 
360 degrees. 

11. The Ecliptic is a great circle in which the sun 
makes his apparent annual progress among the fixed 
stars ; or it is the real path of the earth round the sun, 
and cuts the equinoctial in an angle of 23° 28' ; the 
points of intersection are called the equinoctial points. 
The ecliptic is situated in the middle of the zodiac. 

12. The Zodiac, on the celestial globe, is a space 
which extends about eight degrees on each side of the 



8 



DEFINITIONS, &C. 



ecliptic, like a belt or girdle, within which the motion 
of all the planets* are performed. i 

13. Signs of the Zodiac. The ecliptic and zo- 
diac are divided into 12 equal parts, called signs, each 
containing 30 degrees. The sun makes his apparent 
annual progress through the ecliptic, at the rate of 
nearly a degree in a day. The names of the signs, 
and the days on which the sun enters them, are as fol- 
low: 



Spring Signs. 
°P Aries, the Ram, 21st 

of March. 
8 Taurus, the Bull, 19th 

of April. 
n Gemini, the Twins, 

20th of May. 



Summer Signs. 
2d Cancer, the Crab, 21st 

of June. 
Si Leo, the Lion, 22d of 

July. 
W Virgo, the Virgin, 22d 

of August. 



These are called northern signs, being north of the 
equinoctial. 



Autumnal Signs. 

=£= Libra, the Balance, 
23d of September. 

% Scorpio, the Scor- 
pion, 23d of October. 

t Sagittarius, the Ar- 
cher, 22d of No- 



Winter Signs. 

YS Capricornus, the Goat, 
21st December. 

~ Aquarius, the Water- 
bearer, 20th of January* 

X Pisces, the Fishes, 19th 
February. 



vember. 

These are called southern signs. 
The spring and winter signs are called ascending 
signs ; because when the sun is in any of these, he 

* Except the new discovered planets, or asteroids, Ceres, Pallas, and 
Juno. 



DEFINITIONS, &C. 9 

is ascending towards our pole. The summer and au- 
tumn signs are called descending signs, because when 
the sun is in any of these, he is descending or rece- 
ding from our pole. 

14. The Colures are two great circles passing 
through the poles of the world ; one of them passes 
through the equinoctial points, Aries and Libra ; the 
other through the solstitial points, Cancer and Capri- 
corn ; hence they are called the equinoctial and solsti- 
tial colures. They divide the ecliptic into four equal 
parts, and mark the four seasons of the year, 

15. Declination of the sun, of a star, or planet, is 
its distance from the equinoctial, northward or south- 
ward. When the sun is in the equinoctial he has no 
declination, and enlightens half the globe from pole to 
pole. As he increases in north declination he gradu- 
ally shines farther over the north pole, and leaves the 
south pole in darkness : in a similar manner, when he 
has south declination, he shines over the south pole, 
and leaves the north pole in darkness. The greatest 
declination the sun can have is 23° 28' : the greatest 
declination a star can have is 90°, and that of a planet 
30° 28'* north or south. 

16. The Tropics are two small circles, parallel to 
the equator (or equinoctial,) at the distance of 23° 28' 
from it ; the northern is called the tropic of Cancer, 
the southern the tropic of Capricorn. The tropics are 
the limits of the torrid zone, northward and southward. 

17. The Polar Circles are two small circles, paral- 

* Except the planets, or asteroids, Ceres, Pallas, and Juno, which 
are nearly at the same distance from the sun ; the former, in April 1802, 
was out of the zodiac, its latitude being 15° W N. 



10 DEFINITIONS, &C. 

lei to the equator (or equinoctial,) at the distance of 
66° 32' from it, and 23° 28' from the poles. The 
northern is called the arctic, the southern the antarctic 
circle. 

18. Parallels of Latitude are small circles drawn 
through every ten degrees of latitude, on the terres- 
trial globe, parallel to the equator. Every place on the 
globe is supposed to have a parallel of latitude drawn 
through it, though there are generally only sixteen 
parallels of latitude drawn on the terrestrial globe. 

19. The Hour Circle on the artificial globes is a 
small circle of brass, with an index or pointer fixed to 
the north pole ; it is divided into 24 equal parts, cor- 
responding to the hours of the day, and these are again 
subdivided into halves and quarters. The hour circle 
when placed under the brass meridian, is moveable 
round the axis of the globe, and the brass meridian, in 
this case, answers the purpose of an index. 

20. The Horizon is a great circle which separates 
the visible half of the heavens from the invisible ; the 
earth being considered as a point in the centre of the 
sphere of the fixed stars. Horizon, when applied to 
the earth, is either sensible or rational. 

21. The Sensible, or visible horizon, is the circle 
which bounds our view, where the sky appears to touch 
the earth or sea. 

22. The Rational, or true horizon, is an imaginary 
line passing through the centre of the earth parallel to 
the sensible horizon. It determines the rising and 
setting of the sun, stars, and planets. 

23. The Wooden Horizon, circumscribing the ar- 



DEFINITIONS, &C 11 

tificial globe, represents the rational horizon on the real 
globe. This horizon is divided into several concentric 
circles, which on Bardirfs New British Globes are ar- 
ranged in the following order : 

The First is marked amplitude, and is numbered 
from the east towards the north and south, from to 
90 degrees, and from the west towards the north and 
south in the same manner. 

The Second is marked azimuth, and is numbered 
from the north point of the horizon towards the east 
and west, from to 90 degrees : and from the south 
point of the horizon towards the east and west in the 
same manner. 

The Third contains the 32 points of the compass, 
divided into half and quarter points. The degrees in 
each point are to be found in the amplitude circle. 

The Fourth contains the twelve signs of the zodiac, 
with the figure and character of each sign. 

The Fifth contains the degrees of the signs, each 
sign comprehending 30 degrees. 

The Sixth contains the days of the month answering 
to each degree of the sun's place in the ecliptic. 

The Seventh contains the equation of time, or differ- 
ence of time shown by a well-regulated clock and a 
correct sun-dial. When the clock ought to be faster 
than the dial, the number of minutes, expressing the 
difference, is followed by the sign + ; when the clock 
or watch ought to be slower, the number of minutes in 
the difference is followed by the sign — . 

The Eighth contains the twel v< * calendar months. 



12 DEFINITIONS, &C. 

24. The Cardinal Points of the horizon are east, 
west, north, and south. 

25. The Cardinal Points in the heavens are the 
zenith, the nadir, and the points where the sun rises 
and sets. 

26. The Cardinal Points of the ecliptic are the 
equinoctial and solstitial points, which mark out the 
four seasons of the year ; and the Cardinal Signs are 
<¥> Aries, s Cancer, =2= Libra, and Y5 Capricorn. 

27. The Zenith is a point in the heavens exactly 
over our heads, and is the elevated pole of our horizon. 

28. The Nadir is a point in the heavens exactly 
under our feet, being the depressed pole of our horizon, 
and the zenith, or elevated pole, of the horizon of our 
antipodes. 

29. The Pole of any circle is a point on the surface 
of the globe, 90 degrees distant from every part of that 
circle of which it is the pole. Thus the poles of the 
earth are 90 degrees from every part of the equator ; 
the poles of the ecliptic (on the celestial globe) are 90 
degrees from every part of the ecliptic, and 23° 28' 
from the poles of the equinoctial ; consequently they 
are situated in the arctic and antarctic circles. Every 
circle on the globe, whether real or imaginary, has two 
poles diametrically opposite to each other. 

30. The Equinoctial Points are Aries and Libra, 
where the ecliptic cuts the equinoctial. The point 
Aries is called the vernal equinox, and the point Libra 
the autumnal equinox. When the sun is in either of 
these points, the days and nights on every part of the 
globe are equal to each other. 

31. The Solstitial Points are Cancer and Capri- 



DEFINITIONS, &C. 13 

corn. When the sun is in, or near, these points, the 
variation in his greatest altitude is scarcely perceptible 
for several days ; because the ecliptic near these points 
is almost parallel to the equinoctial, and therefore the 
sun has nearly the same declination for several days. 
When the sun enters Cancer, it is the longest day to 
all the inhabitants on the north side of the equator, and 
the shortest day to those on the south side. When the 
sun enters Capricorn it is the shortest day to those who 
live in north latitude, and the longest day to those who 
live in south latitude. 

32. An Hemisphere is half the surface of the globe ; 
every great circle divides the globe into two hemi- 
spheres. The horizon divides the upper from the lower 
hemisphere in the heavens ; the equator separates the 
northern from the southern on the earth ; and the brass 
meridian, standing over any place on the terrestrial 
globe, divides the eastern from the western hemi- 
sphere. 

33. The Mariner's Compass is a representation of 
the horizon, and is used by seamen to direct and as- 
certain the course of their ships. It consists of a cir- 
cular brass box, which contains a paper card, divided 
into 32 equal parts, and fixed on a magnetical needle 
that always turns towards the north. Each point of 
the compass contains 11° 15' or Hi degrees, being 
the 32d part of 360 degrees. 

34. The Variation of the Compass is the devia- 
tion of its points from the corresponding points in the 
heavens. When the north point of the compass is to 
the east of the true north point of the horizon, the va- 

b o 



14 DEFINITIONS, &C. 

riation is cast : if it be to the west, the variation is 
west. 

The learner is to understand, that the compass does not always point 
directly north, but is subject to a small (irregular) annual variation. 
At present, 1830, in England, the needle points about 24£ degrees to 
the westward of the north. 

The compass is used for setting the artificial globe north and south ; 
but care must be taken to make a proper allowance for the variation. 

35. Latitude of a Place, on the terrestrial globe, 
is its distance from the equator in degrees, minutes, or 
geographical miles, &c. and is reckoned on the brass 
meridian, from the equator towards the north or south 
pole. 

36. Latitude of a Star or Planet, on the celes- 
tial globe, is its distance from the ecliptic, northward 
or southward, counted towards the pole of the ecliptic, 
on the quadrant of altitude. The greatest latitude a 
star can have is 90 degrees, and the greatest latitude of 
a planet is nearly 8 degrees.* The sun being always 
in the ecliptic, has no latitude. 

37. The Quadrant of Altitude is a thin flexi- 
ble piece of brass divided upwards fromO to 90 degrees 
and -downwards from to 18 degrees, and when used is 
generally screwed to the brass meridian. The upper 
divisions are used to determine the distances of places 
on the earth, the distances of the celestial bodies, their 
altitudes, &c. and the lower divisions are applied to 
finding the beginning, end, and duration of twilight. 

38. Longitude of a Place, on the terrestrial globe, 
is the distance of the meridian of that place from the 
first meridian, reckoned in degrees and parts of a de- 

* The newly-discovered planets, or Asteroids, Ceres and Pallas, &c. 
do not appear to be confined within this limit. 



DEFINITIONS, &C. 15 

gree on the equator. Longitude is either eastward or 
westward, according as the place is eastward or west- 
ward of the first meridian. The greatest longitude 
that a place can have is 180 degrees, or half the cir- 
cumference of the globe. 

39. Longitude of a Star, or Planet, is reckoned 
on the ecliptic from the point Aries, eastward, round 
the celestial globe. The longitude of the sun is what 
is called the sun's place on the terrestrial globe. 

40. Almacantars, or parallels of latitude, are ima- 
ginary circles parallel to the horizon, and serve to show 
the height of the sun, moon, or stars. These circles 
are not drawn on the globe, but they may be described 
for any latitude by the quadrant of altitude. 

41. Parallels of Celestial Latitude are small 
circles drawn on the celestial globe parallel to the 
ecliptic. 

42. Parallels of Declination are small circles 
parallel to the equinoctial on the celestial globe, and 
are similar to the parallels of latitude on the terrestrial 
globe. 

43. Azimuth, or Vertical Circles, are imaginary 
great circles passing through the zenith and the nadir, 
cutting the horizon at right angles. The altitudes of 
the heavenly bodies are measured on these circles, 
which circles may be represented by screwing the quad- 
rant of altitude on the zenith of any place, and making 
the other end move along the wooden horizon of the 
globe. 

44. The Prime Vertical is that azimuth circle 
which passes through the east and west points of the 



16 DEFINITIONS, &C. 

horizon, and is always at right angles to the brass me- 
ridian, which may be considered as another vertical 
circle passing through the north and south points of 
the horizon, 

45. The Altitude of any object in the heavens is an 
arc of a vertical circle, contained between the centre 
of the object and the horizon. When the object is upon 
the meridian, this arc is called the meridian altitude. 

46. The Zenith Distance of any celestial object 
is the arc of a vertical circle, contained between the 
centre of that object and the zenith ; or it is what the 
altitude of the object wants of 90 degrees. When the 
object is on the meridian, this arc is called the meri- 
dian zenith distance. 

57. The Polar Distance of any celestial object is 
an arc of a meridian, contained between the centre of 
that object and the pole of the equinoctial. 

48. The Amplitude of any object in the heavens is 
an arc of the horizon, contained between the centre of 
the object when rising, or setting, and the east or west 
points of the horizon. Or, it is the distance which the 
sun or a star rises from the east, and sets from the west, 
and is used to find the variation of the compass at sea. 
When the sun has north declination, it rises to coun- 
tries in north latitudes, to the north of the east, and 
sets to the north of the west ; and when it has south 
declination, it rises to the south of the east, and sets 
to the south of the west. At the time of the equinoxes, 
when the sun has no declination, viz. on the 21st of 
March, and on the 23d of September, it rises exactly 
in the east, and sets exactly in the west. 



DEFINITIONS, &C. 17 

49. The Azimuth of any object in the heavens is 
an arc of the horizon, contained between a vertical cir- 
cle passing through the object, and the north or south 
points of the horizon. The azimuth of the sun, at any 
particular hour, is used at sea for finding the variation 
of the compass. 

50. Hour Circles, or Horary Circles, are the 
same as the meridians. They are drawn through every 
15 degrees* of the equator, each answering to an hour 
— consequently every degree of longitude answers to 
four minutes of time, every half degree to two minutes, 
and every quarter of a degree to one minute. 

On the globes these circles are supplied by the brass 
meridian, the hour circle, and its index. 

51. Positions of the Sphere are three : right, 
parallel, and oblique. 

52. A Right Sphere is that position of the earth 
where the equinoctial passes through the zenith and 
the nadir, the poles being in the rational horizon. The 
inhabitants who have this position of the sphere, live at 
the equator : it is called a right sphere, because the 
parallels of latitude cut the horizon at right angles. In 
a right sphere the parallels of latitude are divided into 
two equal parts by the horizon, and the days and nights 
are of equal length. 

53. A Parallel Sphere is that position the earth 
has when the rational horizon coincides with the equa- 
tor, the poles being in the zenith and nadir. The in- 
habitants who have this position of the sphere (if there 

* On Gary's large Globes the meridians are drawn through every 10 
degrees, as on a Map. 

b 2 o 2 



18 DEFINITIONS, &C. 

be any such inhabitants) lrve at the poles ; it is called 
a parallel sphere, because all the parallels of latitude 
are parallel to the horizon. In a parallel sphere the 
sun appears above the horizon for six months together, 
and he is below the horizon for the same length of 
time. 

54. An Oblique Sphere is that position the earth 
has when the rational horizon cuts the equator oblique- 
ly, and hence it derives its name. All inhabitants on 
the face of the earth (except those who live exactly at 
the poles or at the equator) have this position of the 
sphere. The days and nights are of unequal lengths, 
the parallels of latitude being divided into unequal 
parts by the rational horizon. 

55. Climate is a part of the surface of the earth 
contained between two small circles parallel to the 
equator, and of such a breadth, that the longest day in 
the parallel nearest the pole, exceeds the longest day 
in the parallel of latitude nearest the equator, by half 
an hour, in the torrid and temperate zones, or by a 
month in the frigid zones ; so that there are 24 climates 
between the equator and each polar circle, and six cli- 
mates between each polar circle and its pole. 

56. A Zone is a portion of the surface of the earth 
contained between two small circles parallel to the 
equator, and is similar to the term climate, for pointing 
out the situations of places on the earth, but less exact ; 
as there arc only five zones, which have been distin- 
guished by particular names ; whereas there are 60 
climates. 

57. The Torrid Zone extends from the tropic of 



DEFINITIONS, &C. 19 

Cancer to the tropic of Capricorn, and is 46° 56' broad. 
This zone was thought by the ancients to be uninhabit- 
ed, because it is continually exposed to the direct rays 
of the sun ; and such parts of the torrid zone as were 
known to them were sandy deserts, as the middle of 
Africa, Arabia, &c; and these sandy deserts extend be- 
yond the left bank of the Indus, toward Agimere. 

58. The Two Temperate Zones. The north tem- 
perate zone extends from the tropic of Cancer to the 
arctic circle ; and the south temperate zone from the 
tropic of Capricorn to the antarctic circle. These 
zones are each 43° 4' broad, and were called temper- 
ate by the ancients, because meeting the sun's rays 
obliquely, they enjoy a moderate degree of heat. 

59. The Two Frigid Zones. The north frigid 
zone, or rather segment of the sphere, is bounded by 
the arctic circle. The north pole, which is 23° 28' 
from the arctic circle, is situated in the centre of this 
zone. The south frigid zone is bounded by the antarc- 
tic circle, distant\23° 28' from the south pole, which 
is situated in the centre of this zone. 

60. Ampiiiscii are the inhabitants of the torrid zone ; 
so called, because their shadows fall north or south at 
different times of the year ; the sun being sometimes 
to the south of them at noon, and at other times to the 
north. When the sun is vertical, or in the zenith, 
which happens twice in the year, the inhabitants have 
no shadow, and are then called Aschii, or shadowless. 

61. Heteroscii is a name given to the inhabitants 
of the temperate zones, because their shadows at noon 
fall only one way. Thus, the shadow of an inhabitant 



20 DEFINITIONS, &C 

of the north temperate zone always falls to the north 
at noon, because the sun is then due south; and the 
shadow of an inhabitant of the south temperate zone 
falls towards the south at noon, because the sun is due 
north at that time. 

62. Periscii are those people who inhabit the frigid 
zones, so called, because their shadows, during a revo- 
lution of the earth on its axis, are directed towards 
every point of the compass. In the frigid zones the 
sun does not set during several revolutions of the earth 
on its axis. 

63. Antceci are those who live in the same degree 
of longitude, and in equal degrees of latitude, but the 
one in north and the other in south latitude. They 
have noon at the same time, but contrary seasons of 
the year ; consequently, the length of the days to the 
one, is equal to the length of the nights to the other. 
Those who live at the equator can have no Antceci. 

64. Perioeci are those who live in the same latitude, 
but in opposite longitudes ; when it is noon with the 
one, it is midnight w T ith the other ; they have the same 
length of days, and the same seasons of the year. The 
inhabitants of the poles can have no Perioeci. 

65. Antipodes are those inhabitants of the earth 
who live diametrically opposite to each other, and con- 
sequently walk feet to feet ; their latitudes, longitudes, 
seasons of the year, days and nights, are all contrary to 
each other. 

66. The Right Ascension of the sun, or of a star, 
is that degree of the equinoctial which rises with the 



DEFINITIONS, &C. 2\ 

sun, or star, in a right sphere, and is reckoned from the 
equinoctial point Aries eastward round the globe. 

67. Oblique Ascension of the sun or of a star, is 
that degree of the equinoctial which rises with the sun 
or star, in an oblique sphere, and is likewise counted 
from the point Aries eastward round the globe. 

68. Oblique Descension of the sun, or of a star, is 
that degree of the equinoctial which sets with the sun 
or star in an oblique sphere. 

69. The Ascensional or Descensional Differ- 
ence is the difference between the right and oblique 
ascension, or the difference between the right and 
oblique descension, and, with respect to the sun, it is 
the time he rises before 6 in the spring and summer, or 
sets before 6 in the autumn and winter. 

70. The Crepusculum, or Twilight, is that faint 
light which we perceive before *,he sun rises, and after 
he sets. It is produced by the rays of light being re- 
fracted in their passage through the earth's atmosphere, 
and reflected from the different particles thereof. The 
twilight is supposed to end in the evening when the 
sun is 18 degrees below the horizon, or when stars of 
the sixth magnitude (the smallest that are visible to 
the naked eye) begin to appear ; and the twilight is 
said to begin in the morning, or it is day-break, when 
the sun is again within 18 degrees of the horizon. The 
twilight is the shortest at the equator, and longest at 
the poles ; here the sun is near two months before he 
retreats 18 degrees below the horizon, or to the point 
where his rays are first admitted into the atmosphere ; 



22 DEFINITIONS, &C. 

and he is only two months more before he arrives at 
the same parallel of latitude. 

71. Angle of Position between two places on the 
terrestrial globe, is an angle at the zenith of one of the 
places, formed by the meridian of that place, and a 
vertical circle passing through the other place, being 
measured on the horizon from the elevated pole towards 
the vertical circle: 

The Angle or Position of a Star, is an angle formed by two 
great circles intersecting each other in the place of the star, the one pas- 
sing through the pole of the equinoctial, the other through the pole of 
the ecliptic. 

72. Bayer's Characters. John Bayer, of Augs- 
burg in Swabia, published in 1603 an excellent work, 
entitled Uranometria, being a complete atlas of all the 
constellations, with the useful invention of denoting the 
stars in every constellation by the letters of the Greek 
and Roman Alphabets ; setting the first Greek letter » 
to the principal star in each constellation, £ to the 
second in magnitude, v to the third, and so on, and when 
the Greek alphabet was finished, he began a, ft, c, &c. 
of the Roman. This useful method of describing the 
stars has been adopted by all succeeding astronomers, 
who have farther enlarged it by adding the numbers, 
1, 2, 3, &c. in the same regular succession, when any 
constellation contains more stars than can be marked 
by the two alphabets. The figures are, however, some- 
times placed above the Greek letter, especially where 
double stars occur ; for though many stars may appear 
single to the naked eye, yet when viewed through a 
telescope of considerable magnifying power they ap- 
pear double, triple, &c. Thus, in Dr. Zach's Tabulae 



DEFINITIONS, &C 23 

Motuum Solis, we meet with/Tauri, £ Tauri, r Tauri, 
s* Tauri, ** Tauri, &c. 

As the Greek letters so frequently occur in catalogues of the stars 
and on the celestial globes, the Greek alphabet is here introduced for 
the use of those who are unacquainted with the letters. The capitals 
are seldom used in the catalogues of stars, but are here given for the 
sake of regularity. 

Name. Sound. Name. Sound. 



A 


04 


Alpha 


a 


N 


V 


Nu 


n 


B 


»c 


Beta 


b 


s 


I 


Xi 


X 


r 


r* 


Gamma 


g 








Omicron 


o slvort 


a 


i 


Delta 


d 


n 


IT Zf 


Pi 


P 


E 


■ 


Epsilon 


e short 


p 


€ P 


Rho 


r 


Z 


CC 


Zeta 


z 


s 


<rsC 


Sigma 


s 


H 


>i 


Eta 


e long 


T 


t7 


Tan 


t 





39 


Theta 


th 


r 


u 


Upsilon 


u 


I 


i 


Iota 


i 


o 


<? 


Phi 


ph 


K 


X. 


Kappa 


k 


X 


% 


Chi 


ch 


A 


\ 


Lambda 


1 


t 


* 


Psi 


ps 


M 


t* 


Mu 


m 


£1 


O) 


Omega 


o long. 



73. Diurnal Arc is the arc described by the sun, 
moon, or stars, from their rising to their setting. The 
sun's semi-diurnal arc is the arc described in half the 
length of the day. 

74. Nocturnal Arc is the arc described by the 
sun, moon, or stars, from their setting to their rising. 

75. Aberration is an apparent motion of the ce- 
lestial bodies, occasioned by the earth's annual motion 
in its orbit, combined with the progressive motion of 
light. 



24 



PROBLEMS PERFORMED WITH 



CHAPTER II. 



PROBLEMS PERFORMED WITH THE TERRESTRIAL GLOBE. 

Problem I. 

To find the latitude of any given place. 

Rule. Bring the given place to that part of the 
brass meridian which is numbered from the equator 
towards the poles ; the degree above the place is the 
latitude. If the place be on the north side of the equa- 
tor, the latitude is north ; if it be on the south side the 
latitude is south. 

On small globes the latitude of a place cannot be found nearer than 
to about a quarter of a degree. Each degree of the brass meridian on 
the largest globes is generally divided into three equal parts, each part 
containing twenty geographical miles; on such globes the latitude 
may be found to 10'. 

Examples. — What is the latitude of Edinburgh ? 

Answer. — 56° north. 

2. Required the latitudes of the following places : 

Amsterdam Florence Philadelphia 

Archangel Gibraltar Quebec 

Barcelona Hamburgh Rio Janeiro 

Batavia Ispahan Stockholm 

Bencoolen Lausanne Turin 

Berlin Lisbon Vienna 

Cadiz Madras Warsaw 

Canton Madrid Washington 

Dantzic Naples Wilna 

Drontheim Paris York 



THE TERRESTRIAL GLOBE. 25 

3. Find all the places on the globe which have no 
latitude. 

4. What is the greatest latitude a place can have ? 

Problem II. 

To find all those places which have the same latitude as 
any given place. 

Rule. Bring the given place to that part of the 

brass meridian which is numbered from the equator 

towards the poles, and observe its latitude ; turn the 

globe round, and all places passing under the observed 

latitude are those required. 

All places in the same latitude have the same length of day and 
night, and the same seasons of the year, though from local circumstan- 
ces, they may not have the same atmospherical temperature. 

Examples. 1. What places have the same, or near- 
ly the same latitude as Madrid ? 

Answer. Minorca, Naples, Constantinople, Samarcand, Philadel- 
phia, Pekin, &c. 

2. What inhabitants of the earth have the same 
length of days as the inhabitants of Edinburgh? 

3. What places have nearly the same latitude as 
London ? 

4. What inhabitants of the earth have the same sea- 
sons of the year as those of Ispahan ? 

5. Find all the places of the earth which have the 
longest day the same length as at Port Royal in Ja- 
maica. 

Problem III. 
To find the Longitude of any place* 
Rule. Bring the given place to the brass meridian, 
the number of degrees on the equator, reckoning from 
c p 



26 



PROBLEMS PERFORMED WITH 



the meridian passing through London to the brass me- 
ridian is the longitude. If the place lie to the right 
hand of the meridian passing through London, the lon- 
gitude is east ; if to the Jeft hand, the longitude is 
west. 

On Adams' and Gary's globes there are two rows of figures above 
the equator. When the place lies to the right hand-of the meridian of 
London, the longitudes must be counted on the upper line ; when it 
lies to the left hand it must be counted on the lower line. BardirCs 
New British Globes have also two rows of figures above the equator, 
but the lower line is always used in reckoning the longitude. 

Examples. 1. What is the longitude of Peters- 
burg? 

Answer. 30^° east 

2. What is the longitude of Philadelphia ? 

Answer. 75£° west 

3. Required the longitudes of the following places : 



Aberdeen 

Alexandria 

Barbadoes 

Bombay 

Botany Bay 

Canton 

Carlscrona 

Cayenne 



Civita Vecchia 

Constantinople 

Copenhagen 

Drontheim 

Ephesus 

Gibraltar 

Leghorn 

Liverpool 



Lisbon 

Madras 

Masulipatam 

Mecca 

Nankin 

Palermo 

Pondicherry 

Queda. 



4. What is the greatest longitude a place can have ? 
Problem IV. 

To find all those places that have the same longitude as 
a given place. 



Rule. Bring the given place to the brass meridian ; 



THE TERRESTRIAL GLOBE. 27 

then all places under the same edge of the meridian 
from pole to pole have the same longitude. 

All people situated under the same meridian from 66° 28 north lati- 
tude to 66° 28' south latitude, have noon at the same time; or, if it be 
one, two, three, or any number of hours before or after noon with one 
particular place, it will be the same hour with every other place situa- 
ted under the same meridian. 

Examples. 1. What places have the same, or nearly 
the same longitude as Stockholm ? 

Answer. Dantzic, Presburg, Tarento, the Cape of Good Hope, &c. 

2. What places have the same longitude as Alexan- 
dria? 

3. When it is ten o'clock in the evening at London, 
what inhabitants of the earth have the same hour ? 

4. What inhabitants of the earth have midnight when 
the inhabitants of Jamaica have midnight ? 

5. What places of the earth have the same longitude 
as the following places ? 

London Quebec The Sandwich islands 
Pekin Dublin Pelew islands. 

Problem V. 
To find tlie latitude and longitude of any place. 

Rule. Bring the given place to that part of the 
brass meridian which is numbered from the equator to- 
wards the poles ; the degree above the place is the lati- 
tude, and the degree on the equator, cut by the brass 
meridian, is the longitude. 

This problem is only an exercise of the fir st and third. 

Examples. 1. What are the latitude and longitude 
of Petersburg ? 

Answer. Latitude 60° N. longitude 30i° E. 



28 



PROBLEMS PERFORMED WITH 



2. Required the latitudes and longitudes of the 


lowing places : 






Acapulco 


Cusco 


Lima 


Aleppo 


Copenhagen 


Lizard 


Algiers 


Durazzo 


Lubec 


Archangel 


Elsinore 


Malacca 


Belfast 


Flushing 


Manilla 


Bergen 


Cape Guardafui 


Medina 


Buenos Ayres 


Hamburgh 


Mexico 


Calcutta 


Jeddo 


Mocha 


Candy 


Jaffa 


Moscow 


Corinth 


Ivica 
Problem VI. 


Oporto. 



To find any place on the globe having the latitude and 
longitude of that place given* 

Rule. Find the longitude of the given place on 
the equator, and bring it to that part of the brass me- 
ridian which is numbered from the equator towards 
the poles ; then under the given latitude, on the brass 
meridian, you will find the place required. 

Example's. 1. What place has 1514° east longitude, 
and 34° south latitude ? 

Answer. Botany Bay. 

2. What places have the following latitudes and lon- 
gitudes ? 



Latitudes. 


Longitude. 


Latitude. 


Longitude. 


50° 6' N. 


5° 54' W. 


19° 26' N. 


100° 6' W. 


48 12 N. 


16 16 E. 


59 56 N. 


30 19 E. 


55 58 N. 


3 12 W. 


13 S. 


77 55 W. 


52 22 N. 


4 51 E. 


46 55 N. 


69 53 W 


31 13 N. 


29 55 E. 


59 21 N. 


18 4E. 



THE TERRESTRIAL GLOBE. 29 



64° 


34' N. 


38° 58' E. 


8° 32' N. 


81° 


he. 


34 


29 S. 


18 23 E. 


5 9S. 


119 


49 E. 


3 


49 S. 


102 10 E. 


22 54 S. 


42 


44 W. 


34 


35 S. 


58 31 W. 


36 5 N. 


5 


22 W 


32 


25 N. 


52 50 E. 


32 38 N. 


17 


6W 






Problem VII. 







To find the difference of latitude between any two places* 

Rule. Bring one of the places to that half of the 
brass meridian which is numbered from the equator 
towards the poles, and mark the degree above it ; then 
bring the other place to the meridian, and the number 
of degrees between it and the above mark will be the 
difference of latitude. 

Or, Find the latitudes of both the places (by Prob. 
1.) then, if the latitudes be both north or both south, 
subtract the less latitude from the greater, and the re- 
mainder will be the difference of latitude ; but, if the 
latitudes be one north and the other south, add them 
together, and their sum will be the difference of lati- 
tude. 

Examples. 1. What is the difference of latitude 
between Philadelphia and Petersburgh ? 

Answer. 20 degrees. 

2. What is the difference of latitude between Mad- 
rid and Buenos Ayres ? 

Answer. 75 degrees. 

3. Required the difference of latitude between the 
following places ? 

London and Rome Alexandria and the Cape 

Delhi and Cape Comorin of Good Hope 

c 2 P 2 



30 PROBLEMS PERFORMED WITH 

Vera Cruz and Cape Horn Pekin and Lima 

Mexico and Botany Bay St. Salvador and Surinam 

Astracan and Bombay Washington and Quebec 

St. Helena and Manilla Porto Bello and the Straits 
Copenhagen and Toulon of Magellan • 

Brest and Inverness Trinidad I. and Trincomale 

Cadiz and Sierra Leone Bencoolen and Calcutta. 

4. What two places on the globe have the greatest 
difference of latitude ? 

Problem VIII. 

To find the difference of longitude between any two 

places. 

Rule. Bring one of the given places to the brass 
meridan, and mark its longitude on the equator ; then 
bring the other place to the brass meridian, and the 
number of degrees between its longitude and the above 
mark, counted on the equator, the nearest way round 
the globe, will show the difference of longitude. 

Or, Find the longitudes of both the places (by Prob. 
III.) then, if the longitudes be both east or both west, 
subtract the less longitude from the greater, and the 
remainder will be the difference of longitude : but, if 
the longitude be one east and the other west, add them 
together, and their sum will be the difference of lon- 
gitude. 

When this sum exceeds 180 degrees, take it from 
360, and the remainder will be the difference of lon- 
gitude. 

Examples. 1. What is the difference of longitude 
between Barbadoes and Cape Verd ? 



THE TERRESTRIAL GLOBE. 31 

Answer. 43° 42'. 

2. What is the difference of longitude between 
Buenos Ayres and the Cape of Good Hope ? 

Answer. 76° 54' 

3. What is the difference of longitude between 
Botany Bay and O'why'ee ? 

Answer. 52° 45', or 52$ degrees. 

4. Required the difference of longitude between the 
following places : 

Vera Cruz and Canton Constantinople and Batavia 

Bergen and Bombay Bermudas I. and I. of Rhodes 

Columbo and Mexico Port Patrick and Berne 

Juan Fernandes I. and Mount Heckla and Mount 

Manilla Vesuvius 

Pelew I. and Ispahan Mount ^Etna and Teneriffe 

Boston in Amer. and North Cape and Gibraltar. 

Berlin 

5. What is the greatest difference of longitude com- 
prehended between two places ? 

Problem IX. 

To find the distance bettveen any two places. 

Rule. The shortest distance between any two 
places on the earth, is an arc of a great circle contained 
between the two places. Therefore, lay the graduated 
edge of the quadrant of altitude over the two places, so 
that the division marked may be on one of the places, 
the degrees on the quadrant comprehended between 
the two places will give their distance ; and if these 
degrees be multiplied by 60, the product will give the 
distance in geographical miles ; or multiply the de- 



32 



PROBLEMS PERFORMED WITH 



grees by 69|, and the product will give the distance in 
English miles. 

Or, Take the distance between the two places with 
a pair of compasses, and apply that distance to the equa- 
tor, which will show how many degrees it contains. 

If the distance between the two places should exceed 
the length of the quadrant, stretch a piece of thread 
over the two places, and mark their distance ; the ex- 
tent of thread between these marks, applied to the 
equator, from the meridian of London, will show the 
number of degrees between the two places. 

Examples. 1. What is the nearest distance be- 
tween the Lizard and the island of Bermudas ? 



45? distance in degrees. 
60 


45£ distance in degrees 
69£ 


2700 
30 
15 


22} 
405 
270 
341 
17i 


2745 geographical miles. 




3176f English miles. 



2. What is the nearest distance between the island 
of Bermudas and St. Helena ? 



73£ distance in degrees. 
60 



4380 
30 



4410 geographical miles. 



73£ distance in degrees. 
69* 



365 
657 
438 
34£ 



5108| English miles. 



3. What is the nearest distance between London 
and Botany Bay. 



1">J distance in degrees. 
00 



THi: TERRESTRIAL GLOBE. 

54 ( 
69i 



V2M) geographical miles. 



154 distance In degrees. 



77 
1380 
924 



10703 English miles. 



4. What is the direct distance between London and 
Jamaica, in geographical and English miles? 

5. What is the extent of Europe in English miles, 
from Cape Matopan in the Morea, to the North Cape 
in Lapland ? 

6. What is the extent of Africa from Cape Verd to 
Cape Guardafui ? 

7. What is the extent of south America from Cape 
Blanco in the west to Cape St. Roque in the east ? 

8. Suppose the track of a ship to Madras be from 
the Lizard to St. Anthony, one of the Cape Verd is- 
lands, thence to St. Helena, thence to the Cape of Good 
Hope, thence to the east of the Mauritius, thence a 
little to the south-east of Ceylon, and thence to Madras ; 
how many English miles is the Land's End from Mad- 
ras? 

Pkoblem X. 

A 'place being given on the globe, to find all places, 
which are situated at the same distance from it as 
any other given place. 

Rule. Lay the graduated edge* of the quadrant of 
altitude over the two places, so that the division marked 
may be on one of the places, then observe what de- 
gree of the quadrant stands over the other place ; move 
the quadrant entirely round, keeping the division mark- 



34 PROBLEMS PERFORMED WITH 

ed in its. first situation, and all places which pass 
under the same degree which was observed to stand 
over the other place, will be those sought. 

Or, Place one foot of a pair of compasses in one of 
the givon places, and extend the other foot to the other 
given place : a circle described from the first place as 
a centre, with this extent, will pass through all the pla- 
ces sought. 

If the distance between the two given places should exceed the 
length of the quadrant, or the extent of a pair of compasses, stretch a 
piece of thread over the two places, as in the preceding problem. 

Examples. 1. It is required to find all the places on 
the globe which are situated at the same distance from 
London as Warsaw is ? 

Answer. Koningsburg, Buda, Posega, Alicant, &c. 

2. What places are at the same distance from Lon- 
don as Petersburg is ? 

3. What places are at the same distance from Lon- 
don as Constantinople is ? 

4. What places are at the same distance from Rome 
as Madrid is ? 

Problem XL 
Given the latitude of a place and its distance from a 

given place, to find that place whereof the latitude is 

given. 

Rule. If the distance be given in English or geo- 
graphical miles, turn them into degrees by dividing by 
69| for English miles, or 60 for geographical miles ; 
then put that part of the graduated edge of the quad- 
rant of altitude which is marked upon the given place, 
and move the other end eastward or westward (accord- 
ing as the required place lies to the east or west of 



THE TERRESTRIAL GLOBE. 35 

the given place,) till the degrees of distance cut the 
given parallel of latitude : under the point of intersec- 
tion you will find the place sought. 

Or, Having reduced the miles into degrees, take 
the same number of degrees from the equator with a 
pair of compasses, and with one foot of the compass in 
the given place, as a centre, and his extent of degrees, 
describe a circle on the globe ; turn the globe till this 
circle falls under the given latitude on the brass meri- 
dian, and you will find the place required. 

Examples. 1. A place in latitude 60° N. is 1320$ 
English miles from London, and it is situated in E. 
longitude ; required the place ? 

Answer. Divide 1320£ miles by 69? miles, or which is the same 
thing, 2641 half-miles by 139 half-miles, the quotient will give 19 de- 
grees ; hence the required place is Petersburgh. 

2. A place in latitude 32$° N. is 1350 geographical 
miles from London, and it is situated in W. longitude; 

required the place ? 

Answer. Divide 1350 by 60, the quotient is 22° 30 7 , or 22£ degrees ; 
hence the required place is the west point of the island of Madeira. 

3. What place in E. longitude and 41° N. latitude, 
is 1529 English miles from London ? 

4. What place in W. longitude and 13° N. latitude, 
is 3660 geographical miles from London ? 

Problem XII. 

Given the longitude of a place and its distance from a 
given place, to find that place whereof the longitude 
is given. 

Rule. If the distance be given in English or geo- 
graphical miles, turn them into degrees by dividing by 



36 PROBLEMS PERFORMED WITH 

69| for English miles, or 60 for geographical miles; 
then put that part of the graduated edge of the quad- 
rant of altitude which is marked upon the given 
place, and move the other end northward or southward 
(according as the required place lies to the north or 
south of the given place,) till the degrees of distance 
cut the given longitude : under the point of intersec* 
tion you will find the place sought. 

Or, Having reduced the miles into degrees, take 
the same number of degrees from the equator with a 
pair of compasses, and with one foot of the compasses 
in the given place, as a centre, and this extent of de- 
grees, describe a circle on the globe ; bring the given 
longitude to the brass meridian, and you will find the 
place, upon the circle, under the brass meridian. 

Examples. 1. A place in north latitude, and in 60 
degrees west longitude, is 4239^ English miles from 
London ; required the place ? 

Answer. Divide 4239£ miles by 69| miles, or, which is the same 
thing, 8479 half-miles by 139 half-miles, the quotient will give 61 de- 
grees ; hence the required place is the island of Barbadoes. 

2. A place in north latitude, and in 75J degrees 
west longitude, is 3120 geographical miles from Lon- 
don ; what place is it ? 

3. A place in 31i degrees east longitude, and situ- 
ated southward of London, is 2224 English miles from 
it ; required the place ? 

4. A place in 29 degrees east longitude, and situa- 
ted southward of London, is 1529 English miles from 
it ; required the place ? 



THE TERRESTRIAL GLOBE. 37 



Problem XIII. 



To find how many miles make a deg. of longitude in any 
given parallel of latitude. 

Rule. Lay the quadrant of altitude parallel to the 
equator, between any two meridians in the given lati- 
tude, which differ in longitude 15 degrees ; the num- 
ber of degrees intercepted between them multiplied by 
4, will give the length of a degree in geographical 
miles. The geographical miles may be brought into 
English miles by multiplying by 116, and cutting off 
two figures from the right-hand of the product. 

Or, Take the distance between two meridians, which 
differ in longitude 15 degrees in the given parallel of 
latitude, with a pair of compasses ; apply this distance 
to the equator, and observe how many degrees it makes : 
with which proceed as above. 

Since the quadrant of altitude will measure no arc truly but that of 
a great circle ; and a pair of compasses will only measure the chord of 
an arc, not the arc itself; it follows that the preceding rule cannot be 
mathematically true, though sufficiently correct for practical purposes. 
When great exactness is required, recourse must be had to calculation. 

The above rule is founded on a supposition that the number of de- 
grees contained between any two meridians, reckoned on the equator 
is to the number of degrees contained between the same meridians, on 
any parallel of latitude, as the number of geographical miles contained 
in one degree of the equator, is to the number of geographical miles 
contained in one degree on the given parallel of latitude. Thus in the 
latitude of London, two places which differ 15 degrees in longitude are 
9£ degrees distant by the rule. Hence, 

15o : 9h : : 60m. : 37m.; or 15° : 60m. : : 9£ : 37m.; but 15 is to 60 as 1 
is to 4, therefore, 1 : 4 : : 9£ : 37 geographical miles contained in one de- 
gree. Now, any number of geographical miles may be brought into 
English miles by multiplying by 69£ and dividing by 60 ; or by multi- 
plying by 1.16; for 60: 69£ : : 1.16 nearly. 

d Q 



38 PROBLEMS PERFORMED WITH 

Examples. 1. How many geographical and English 
miles make a degree in the latitude of Pekin ? 

Answer. The latitude of Pekin is 40° north : the distance between 
two meridians in that latitude (which differ in longitude 15 degrees) is 
Hi degrees. .Now, 111 degrees multiplied by 4, produces 46 geogra- 
phical miles for the length of a degree of longitude, in the latitude of 
Pekin; and if 46 be multiplied by 116, the product will be 5336 ; cut 
oif the two right hand-hand figures, and the length of a degree in Eng- 
lish miles will be 53. Or, by the rule of three, 15° : 69£m. : : ll£ : 
53 miles. 

2. How many miles make a degree in the parallels 
of latitude wherein the following places are situated? 
Surinam Washington Spitzbergen 

Barbadoes Quebec Cape Verd 

Havana Skalholt Alexandria 

Bermudas I. North Cape Paris. 

Problem XIV* 
To find the bearing of one place from another. 

Rule. If both the places be situated on the same 
parallel of latitude, their bearing is either east or west 
from each other ; if they be situated on the same me- 
ridian, they bear north and south from each other ; if 
they be situated on the same rhumb-line, that rhumb- 
line is their bearing : if they be not situated on the 
same rhumb-line, lay the quadrant of altitude over the 
two places, and that rhumb-line which is the nearest of 
being parallel to the quadrant will be their bearing. 

Or, If the globe have no rhumb-lines drawn on it, 
make a small mariner's compass (such as in Plate I. 
fig. 4.) and apply the centre of it to any given place, 
so that the north and south points may coincide with 
some meridian ; the other points will show the bearings 
of all the circumjacent places, to the distance of up- 



THE TERRESTRIAL GLOBE. 



39 



wards of a thousand miles, if the centrical place be not 
far distant from the equator. 

Exa3iples. 1. Which way must a ship steer from 
the Lizard to the island of Bermudas ? 

Answer. W. S. W. 

2. Which way must a ship steer from the Lizard to 
the island of Madeira? 

Answer. S. S. VV. 

3. Required the bearing between London and the 
following places ? 



Amsterdam 


Copenhagen 


Petersburg 


Athens 


Dublin 


Prague 


Bergen 


Edinburgh 


Rome 


Berlin 


Lisbon 


Stockholm 


Berne 


Madrid 


Vienna 


Brussels 


Naples 


Warsaw. 


Buda 


Paris 
Problem XV. 





To find the angle of position between two places. 

Rule. Elevate the north or south pole, according 
as the latitude is north or south, so many degrees 
above the horizon as are equal to the latitude of one of 
the given places ; bring that place to the brass meri- 
dian, and screw the quadrant of altitude upon the de- 
gree over it ; next move the quadrant till its graduated 
edge falls upon the other place ; then the number of 
degrees on the wooden horizon, between the graduated 
edge of the quadrant and the brass meridian, reckoning 
towards the elevated pole, is the angle of position be- 
tween the two places. 



40 PROBLEMS PERFORMED WITH 

Examples. 1. What is the angle of position between 
London and Prague ? 

Answer. 90 degrees from the north towards the east : the quadrant 
of altitude will fall upon the east point of the horizon, and pass over 
or near the following places, viz. Rotterdam, Frankfort, Cracow, Ock- 
zakov, Caffa, south part of the Caspian Sea, Guzerat in India, Madras, 
and part of the island of Ceylon. Hence all these places have the 
same angle of position from London. 

2. What is the angle of position between London 
and Port Royal in Jamaica ? 

Answer. 90 degrees from the north towards the west ; the quadrant 
of altitude will fall upon the west point of the horizon. 

3. What is the angle of position between Philadel- 
phia and Madrid? 

Answer. 65 degrees from the north towards the east ; the quadrant 
of altitude will fall between the E. N. E. and N. E. by E. points of the 
horizon. 

4. Required the angles of position between London 
and the following places? 

Amsterdam Copenhagen Rome 

Berlin Cairo Stockholm 

Berne Lisbon Petersburg 

Constantinople Madras Quebec. 

Problem XVI. 

To find the Antceci, Perioeci, and Antipodes to the 
inhabitants of any place. 

Rule. Place the two poles of the globe in the hori- 
zon, and bring the given place to the eastern part of 
the horizon ; then, if the given place be in north lati- 
tude, observe how many degrees it is to the northward 
of the east point of the horizon ; the same number of 
degrees to the southward of the east point will show 



THE TERRESTRIAL GLOBE. 41 

the Antoeci ; an equal number of degrees, counted from 
the west point of the horizon towards the north, will 
show the Perioeci ; and the same number of degrees, 
counted towards the south of the west, will point out 
the Antipodes. If the place be in south latitude, the 
same rule will serve by reading south for north, and the 
contrary. 

Or thus : 

For the Antceci. Bring the given place to the brass 
meridian and observe its latitude ; then in the opposite 
hemisphere, under the same degree of latitude, you 
will find the Antceci. 

For the Perioeci. Bring the given place to the brass 
meridian, and set the index of the hour circle to 12, 
turn the globe half round, or till the index points to the 
other 12 ; then under the latitude of the given place 
you will find the Perioeci. 

For the Antipodes. Bring the given place to the 
brass meridian, and set the index of the hour circle to 
12, turn the globe half round, or till the index points 
to the other 12 ; then under the same degree of latitude 
with the given place, but in the opposite hemisphere, 
you will find the Antipodes. 

Examples. 1. Required the Antoeci, Perioeci, and 
Antipodes, to the inhabitants of the island of Bermu- 
das? 

Answer. Their Antoeci are situated in Paraguay, a little N. W. of 
Buenos Ayres ; their Perioeci in China, N W of Nankin ; and their 
Antipodes in the S. W. part of New Holland. 

2. Required the Antceci, Perioeci, and Antipodes to 
the inhabitants of the Cape of Good Hope ? 
d 2 Q 2 



42 PROBLEMS PERFORMED WITH 

3. Captain Cook, in one of his voyages, was in 50 
degrees south latitude and 180 degrees of longitude; 
in what part of Europe were his Antipodes ? 

4. Required the Antceci to the inhabitants of the 
Falkland islands? 

5. Required the Perioeci to the inhabitants of the 
Philippine islands ? 

6. What inhabitants of the earth are Antipodes to 
those of Buenos Ayres ? 

To find at what rate per hour the inhabitants of any 
given place are carried, from west to east, by the re- 
volution of the earth on its axis. 
Rule. Find how many miles make a degree of 
longitude in the latitude of the given place (by Prob- 
lem XIII.) which multiply by 15 for the answer. 

Or, look for the latitude of the given place in the 
table, Problem IX., against which you will find the 
number of miles contained in one degree ; multiply 
these miles by 15, and reject two figures from the right 
hand of the product ; the result will be the answer. 

Examples. 1. At what rate per hour are the in- 
habitants of Madrid carried from west to east by the 
revolution of the earth on its axis? 

Answer. The latitude of Madrid is about 40° N. where a degree of 
longitude measures 46 geographical, or 53 English miles (see Example 
1. Prob. XIII.) Now 46 multiplied by 15 produces 690; and 53 multi- 
plied by 15 produces 795; hence the inhabitants of Madrid are carried 
690 geographical, or 795 English miles per hour. 

By the Table. Against the latitude 40 you will find 45-96 geogra- 
phical miles, and 52-85 English miles : Hence, 

44-95 X 15 = 689- 10 and 52-85 X 15 = 792-75, by rejecting the two right- 
hand figures from each product, the result will be 689 geographical 
miles, and 792 English miles, agreeing nearly with the above. 



THE TERRESTRIAL GLOBE. 43 

2. At what rate per hour are the inhabitants of the 
following* places carried from west to east by the revo- 
lution of the earth on its axis ? 

Skalholt Philadelphia Cape of Good Hope 

Spitzbergen Cairo Calcutta 

Petersburgh Barbadoes Delhi 

London Quito Batavia. 

Problem XVIII. 

A particular place, and the hour of the day at that 
place being given, to find what hour it is at any other 
place. 

Rule. Bring the place at which the time is given 
to the brass meridian, and set the index of the hour 
circle to 12 ; turn the globe till the other place comes 
to the meridian, and the hours passed over by the in- 
dex will be the difference of time between the two 
places. If the place where the hour is sought lie to 
the east of that wherein the time is given, count the 
difference of time forward from the given hour ; if it 
lie to the west, reckon the difference of time backward. 

Or, without the hour circle. 

Find the difference of longitude between the two 
places (by Problem VIII.) and turn it into time by al- 
lowing 15 degrees to an hour, or four minutes of time 
to one degree. The difference of longitude in time 
will be the difference of time between the two places, 
with which proceed as above. Degrees of longitude 
may be turned into time by multiplying by 4 ; observ- 
ing that minutes or miles of longitude, when multiplied 



44 PROBLEMS PERFORMED WITH 

by 4, produce seconds of time ; and degrees of longi- 
tude, when multiplied by 4, produce minutes of time. 

Some globes have two rows of figures on the hour circle, others but 
one : this difference frequently occasions confusion ; and the manner 
in which authors in general direct a learner to solve those problems 
wherein the hour circle is used, serves only to increase that confusion. 
In this, and in all the succeeding problems, great care has been taken 
to render the rules general for any hour circle whatsoever. 

Examples. 1. When it is ten o'clock in the morn- 
ing at London, what hour is it at Petersburgh? 

Answer. The difference of time is two hours ; and, as Petersburg is 
eastward of London, this difference must be counted forward, so that 
it is 12 o'clock at noon at Petersburg. 

Or, the difference of longitude between Petersburgh and London is 
30° 25', which multiplied by 4 produces two hours 1 min. 40 sec. the 
difference of time shown by the clocks of London and Petersburgh . 
hence as Petersburgh lies to the east of London ; when it is ten o'clock 
in the morning at London, it is one minute and 40 seconds past 12 at 
Petersburgh. 

2. When it is two o'clock in the afternoon at Alex- 
andria in Egypt, what hour is it at Philadelphia ? 

Answer. The difference of time is seven hours ; and because Phila- 
delphia lies to the westward of Alexandria, this difference must be 
reckoned backward, so that it is seven o'clock in the morning at Phila* 
phia. 

Or, The longitude of Alexandria is 30° 16' E. 

The longitude of Philadelphia is 75 11 W. 

Difference of longitude 105 27 

4 



Difference of longitude in time 7 h. 1 m. 48 sec. ; 
the clocks at Philadelphia are slower than those of Alexandria ; hence 
when it is two o'clock in the afternoon at Alexandria, it is 58 m. 12 sec. 
past six in the morning at Philadelphia. 

3. When it is noon at London, what hour is it at Cal- 
cutta ? 



THE TERRESTRIAL GLOBE. 45 

4. When it is ten o'clock in the morning at London, 
what hour is it at Washington? 

5. When it is nine o'clock in the morning at Jamai- 
ca, what o'clock is it at Madras ? 

6. My watch was well regulated at London, and 
when I arrived at Madras, which was after a five 
months' voyage, it was four hours and fifty minutes 
slower than the clocks there. Had it gained or lost 
during the voyage ? and how much ? 

Problem XIX. 

A particular place and the hour of the day being given, 
to find all places on the globe where it is then noon, 
or any other given hour. 

Rule. Bring the given place to the brass meridian, 
and set the index of the hour circle to 12 ; then, as the 
difference of time between the given and required 
places is always known by the problem, if the hour at 
the required places be earlier than the hour at the 
given place, turn the globe eastward till the index has 
passed over as many hours as are equal to the given 
difference of time ; but, if the hour at the required 
places be later than the hour at the given place, turn 
the globe westward till the index has passed over as 
many hours as are equal to the given difference of time ; 
and, in each case, all the places required will be found 
under the brass meridian. 

Or, without the hour circle. 

Reduce the difference of time between the given 
place and the required places into minutes; these mi- 



46 PROBLEMS PERFORMED WITH 

nutes, divided by 4, will give degrees of longitude ; if 
there be a remainder after dividing by 4, multiply it by 
60, and divide the product by four, the quotient will 
be minutes or miles of longitude. The difference of 
longitude between the given place and the required 
places being thus determined, if the hour at the re- 
quired places be earlier than the hour at the given 
place, the required places lie so many degrees to the 
westward of the given place as are equal to the differ- 
ence of longitude ; if the hour at the required places 
be later than the hour at the given place, the required 
places lie so many degrees to the eastward of the given 
place as are equal to the difference of longitude. 

Examples. 1. When it is noon at London, at what 
places is it half past eight o'clock in the morning ? 

Answer. The difference of time between London, the given place, 
and the required places, is 3£ hours, and the time at the required places 
is earlier than that at London ; therefore the required places lie 3£ hours 
westward of London ; consequently, by bringing London to the brass 
meridian, setting the index to 12, and turning the globe eastward till the 
index has passed over 3£ hours, all the required places will be under 
the brass meridian, as the eastern coast of Newfoundland, Cayenne, part 
of Paraguay, &c. 

Or, The difference of time between London, the given place, and the 
required places, is 3 hours 30 min. 

3h. 30 m. The difference of longitude between the 

60 given place and the required places is 52° 30' 

The hour at the required places being earlier 

4)120 m. than that at the given place, they lie 52° 30' 

• westward of the given place. Hence, all 

52° — 2 places situated in 52° 30' west longitude from 

60 London, are the places sought, and will be 

found to be Cayenne, &c. as above. 

4)120 

30 m. 



THE TERBESTBIAL GLOBE. 47 

2. When it is two o'clock in the afternoon at Lon- 
don, at what places is it £ past five in the afternoon? 

Answer. Here the difference of time between London, the given 
place, and the required places, is 3h hours ; but the time at the required 
places is later than at London. The operation will be the same as in 
example 1, only the globe must be turned 3h hours towards the west, 
because the required places will be in east longitude, or eastward of the 
given place. The places sought are the Caspian Sea, western part of 
Nova Zembla, the island of Socotra, eastern part of Madagascar, &c. 

3. When it is % past four in the afternoon at Paris, 
where is it noon? 

4. When it is | past seven in the morning at Ispa- 
han, where is it noon ? 

5. When it is noon at Madras, where it is \ past six 
o'clock in the morning? 

6. At sea in latitude 40° north, when it was ten 
o'clock in the morning by the time-piece which shows 
the hour at London, it was exactly 9 o'clock in the 
morning at the ship, by a correct celestial observation. 
In what part of the ocean was the ship ? 

7. When it is noon at London, what inhabitants of 
the earth have midnight ? 

8. When it is ten o'clock in the morning at London, 
where is it ten o'clock in the evening ? 

Problem XX. 

To find the surfs longitude {commonly called the sun's 
place in the ecliptic) and his declination. 

Rule. Look for the given day in the circle of 
months on the horizon, against which, in the circle of 
signs, are the sign and degree in which the sun is for 
that day. Find the same sign and degree in the eclip- 



48 PROBLEMS PERFORMED WITH 

tic on the surface of the globe ; bring the degree of 
the ecliptic, thus found, to that part of the brass meri- 
dian which is numbered from the equator towards the 
poles ; its distance from the equator reckoned on the 
brass meridian, is the sun's declination. 

This problem may be performed by the celestial globe, 
using the same rule. 

Or, by the analemma. 

Bring the analemma to that part of the brass meri- 
dian which is numbered from the equator towards the 
poles, and the degree on the brass meridian, exactly 
above the day of the month, is the sun's declination. 
Turn the globe till a point of the ecliptic, correspond- 
ing to the day of the month, passes under the degree of 
the sun's declination, that point will be the sun's lon- 
gitude or place for the given day. If the sun's declina- 
tion be north, and increasing, the sun's longitude will 
be somewhere between Aries and Cancer. If the de- 
clination be decreasing, the longitude will be between 
Cancer and Libra. If the sun's declination be south, 
and increasing, the sun's longitude will be between 
Libra and Capricorn ; if the declination be decreasing, 
the longitude will be between Capricorn and Aries. 

The sun's longitude and declination are given in the second page of 
every month, in the Nautical Almanac for every day in that month; 
they are likewise given in White's Ephemeris, for every day in the 
year. 

Examples. 1. What is the sun's longitude and de- 
clination on the 15th of April? 
Answer. The sun's place is 26° in cp, declination 10° N. 



THE TERRESTRIAL GLOBE. 



49 



2. Required the sun's place and declination for the 
following days? 



January 21. 


May 18 


September 9. 


February 7. 


June 11 


October 16. 


March 16. 


July 11 


November 17 


April 8. 


August 1. 


December 1. 



Problem XXI. 

To place the globe in the same situation with re- 
spect to the sun, as our earth is at the equi- 
noxes, at the summer solstice, and at the winter 
solstice, and thereby to show the comparative lengths 
of the longest and shortest days* 

1. For the Exuinoxes. Place the two poles of the 
globe in the horizon : for at this time the sun has no 
declination, being in the equinoctial in the heavens, 
which is an imaginary line standing vertically over the 
equator on the earth. Now, if we suppose the sun to 
be fixed, at a considerable distance from the globe, ver- 
tically over that point of the brass meridian which is 
marked 0, it is evident that the wooden horizon will be 
the boundary of light and darkness on the globe, and 
that the upper hemisphere will be enlightened from 
pole to pole. 

* In this problem, as in all others where the pole is elevated to the 
sun's declination, the sun is supposed to be fixed, and the earth to 
move on its axis from west to east. The author of this work has a 
little brass bail made to represent the sun ; this ball is fixed upon a 
strong wire, and when used, slides out of a socket like an acromatie 
telescope. The socket is made to screw to the brass meridian (of any 
globe) over the sun's declination, and the little brass ball representing 
the sun, stands over the declination, at a considerable distance from the 
globe. 

e R 



50 PROBLEMS PERFORMED WITH 

Meridians, or lines of longitude, being generally 
drawn on the globe through every 15 degrees of the 
equator^ the sun will apparently pass from one meri- 
dian to another in an hour. If you bring the point 
Aries on the equator to the eastern part of the horizon, 
the point Libra will be in the western part thereof; 
and the sun will appear to be setting to the inhabitants 
of London * and to all places under the same meridian : 
let the globe be now turned gently on its axis towards 
the east, the sun will appear to move towards the west ; 
and, as the different places successively enter the dark 
hemisphere, the sun will appear to be setting in the 
west. Continue the motion of the globe eastward, till 
London comes to the western edge of the horizon ; the 
moment it emerges above the horizon, the sun will ap- 
pear to be rising in the east. If the motion of the 
globe on its axis be continued eastward, the sun will 
appear to rise higher and higher, and to move towards 
the west ; when London comes to the brass meridian, 
the sun will appear at its greatest height; and after 
London has passed the brass meridian, he will continue 
his apparent motion westward, and gradually diminish 
in altitude till London comes to the eastern part of the 
horizon, when he will again be setting. During this 
revolution of the earth on its axis, every place on its 
surface has been twelve hours in the dark hemisphere, 
and twelve hours in the enlightened hemisphere ; con- 
sequently the days and nights are equal all over the 
world ; for all the parallels of latitude are divided into 



* The meridian of London is nere supposed to pass through the 
equinoctial point Aries, as on the best modern globes. 



THE TERRESTRIAL GLOBE. 51 

two equal parts by the horizon, and in every degree of 
latitude there are six meridians between the eastern 
part of the horizon and the brass meridian ; each of 
these meridians answers to one hour, hence half the 
length of the day is six hours, and the whole length 
twelve hours. 

If any place be brought to the brass meridian, the 
number of degrees between that place and the horizon 
(reckoned the nearest way) will be the sun's meridian 
altitude. Thus, if London be brought to the meridian, 
the sun will then appear exactly south, and its altitude 
will be 38 J degrees ; the sun's meridian altitude at 
Philadelphia will be 50 degrees ; his meridian altitude at 
Quito 90 degrees ; and here, as in every place on the 
equator, as the globe turns on its axis, the sun will be 
vertical. At the Cape of Good Hope the sun will ap- 
pear due north at noon, and his altitude will be 55i 
degrees. 

2. For the Summer Solstice. — The summer sol- 
stice, to the inhabitants of north latitude, happens on 
the 21st of June, when the sun enters Cancer, at which 
time his declination is 23° 28' north. Elevate the 
north pole 23J degrees above the northern point of the 
horizon, bring the sign of Cancer in the ecliptic to the 
brass meridian, and over that degree of the brass meri- 
dian under which this sign stands, let the sun be sup- 
posed to be fixed at a considerable distance from the 
globe. 

While the globe remains in this position, it will be 
seen that the equator is exactly divided into two equal 
parts, the equinoctial point Aries being in the western 



52 PROBLEMS PERFORMED WITH 

part of the horizon, and the opposite point Libra in the 
eastern part, and between the horizon and the brass 
meridian (counting on the equator) there are six meri- 
dians, each fifteen degrees, or an hour apart ; conse- 
quently the day at the equator is twelve hours long. 
From the equator northward as far as the arctic circle, 
the diurnal arcs will exceed the nocturnal arcs; 
that is, more than one half of any of the parallels of 
latitude will be above the horizon, and of course less 
than one half will be below, so that the days are longer 
than the nights. All the parallels of latitude within 
the Arctic circle will be wholly above the horizon, con- 
sequently those inhabitants will have no night. From 
the equator southward, as far as the Antarctic circle, 
the nocturnal arcs will exceed the diurnal arcs ; that 
is, more than one half of any one of the parallels of lati- 
tude will be below the horizon, and consequently less 
than one half will be above. All the parallels of lati- 
tude within the Antarctic circle, will be wholly below 
the horizon, and the inhabitants, if any, will have 
twilight or dark night. 

From a little attention to the parallels of latitude, 
while the globe remains in this position, it will easily 
be seen that the arcs of those parallels which are above 
the horizon north of the equator, are exactly of the 
same length as those below the horizon, south of the 
equator; consequently, when the inhabitants of north 
latitude have the longest day, those in south latitude 
have the longest night. It will likewise appear, that 
the arcs of those parallels which are above the horizon, 
south of the equator, are exactly of the same length as 



THE TERRESTRIAL GLOBE. 53 

those below the horizon, north of the equator ; there- 
fore, when the inhabitants who are situated south of 
the equator have the shortest day, those who Jive north 
of the equator have the shortest night. 

By counting the number of meridians, (supposing 
them to be drawn through every fifteen degrees of the 
equator) between the horizon and the brass meridian, 
on any parallel of latitude, half the length of the day 
will be determined in that latitude, the double of which 
is the length of the day. 

1. In the parallel of 20 degrees north latitude, there 
are six meridians and two thirds more, hence the lon- 
gest day is 13 hours and 20 minutes ; and in the paral- 
lel of 20 degrees south latitude there are five meri- 
dians and one third, hence the shortest day in that lati- 
tude is ten hours and forty minutes. 

2. In the parallel of 30 degrees north latitude, there 
are seven meridians between the horizon and the brass 
meridian, hence the longest day is 14 hours ; and in the 
same degree of south latitude there are only five meri- 
dians, hence the shortest day in that latitude is ten 
hours. 

3. In the parallel of 50 degrees north latitude there 
are eight meridians between the horizon and the brass 
meridian ; the longest day is therefore sixteen hours ; 
and in the same degree of south latitude there are only 
four meridians ; hence the shortest day is eight hours. 

4. In the parallel of 60 degrees north latitude, 

there are 9J meridians from the horizon to the brass 

meridian, hence the longest day is 18^ hours ; and in 

the same degree of south latitude, there are only 2% me- 

e 2 R 2 



54 PROBLEMS PERFORMED WITH 

ridians, the length of the shortest day is therefore 5£ 
hours. 

By turning the globe gently round on its axis from 
west to east, we shall readily perceive that the sun will 
be vertical to all the inhabitants under the tropic 
of Cancer, as the places successively pass the brass 
meridian. 

If any place be brought to the brass meridian, the 
number of degrees between that place and the horizon 
(reckoning the nearest way) will show the sun's meri- 
dian altitude. Thus, at London, the sun's meridian al- 
titude will be found to be about 62 degrees ; at Pe- 
tersburgh 54j degrees, at Madrid 73 degrees, &c. 
To the inhabitants of these places the sun appears due 
south at noon. At Madras the sun's meridian altitude 
will be 79 J degrees, at the Cape of Good Hope 32 de- 
grees, at Cape Horn 10| degrees, &c. The sun will 
appear due north to the inhabitants of these places at 
noon. If the southern extremity of Spitzbergen, in 
latitude 76^ north, be brought to that part of the brass 
meridian which is numbered from the equator towards 
the poles, the sun's meridian altitude will be 37 de- 
grees, which is its greatest altitude ; and if the globe 
be turned eastwards twelve hours, or till Spitzbergen 
comes to that part of the brass meridian which is num- 
bered from the pole towards the equator, the sun's al- 
titude will be ten degrees, which is its least altitude for 
the day given in the problem. It was shown, in the 
foregoing part of the problem, that, when the sun is 
vertically over the equator in the vernal equinox, the 
north pole begins to be enlightened ; consequently the 



THE TERRESTRIAL GLOBE. 55 

farther the sun apparently proceeds in its course north- 
ward, the more day-light will be diffused over the north 
, polar regions, and the sun will appear gradually to in- 
crease in altitude at the north pole, till the 21st of 
June, when his greatest height is 23^ degrees ; he will 
then gradually diminish in height till the 23d of Sep- 
tember, the time of the autumnal equinox, when he 
will leave the north pole, and proceed towards the 
south ; consequently the sun has been visible at the 
north pole for six months. 

3. For the Winter Solstice. — The winter sol- 
stice, to the inhabitants of north latitude, happens on 
the 21st of December, when the sun enters Capricorn, 
at which time his declination is 23° 28' south. Elevate 
the south pole 23| degrees above the southern point of 
the horizon, bring the sign of Capricorn in the ecliptic 
to the brass meridian, and over that degree of the brass 
meridian under which this sign stands, let the sun be 
supposed to be fixed at a considerable distance from 
the globe. 

Here, as at the summer solstice, the days at the equa- 
tor will be twelve hours long, but the equinoctial point 
Aries will be in the eastern part of the horizon, and 
Libra in the western. From the equator southward, 
as far as the Antarctic circle, the diurnal arcs will ex- 
ceed the nocturnal arcs. All the parallels of latitude 
within the Antarctic circle will be wholly above the 
horizon. From the equator northward, the nocturnal 
arcs will exceed the diurnal arcs. All the parallels of 
latitude within the Arctic circle will be wholly below 
the horizon. The inhabitants south of the equator 



56 PROBLEMS PERFORMED WITH 

will now. have their longest day, while those on the 
north of the equator will have their shortest day. 

As the globe turns on its axis from west to east, the 
sun will be vertical successively to all the inhabitants 
under the tropic of Capricorn. By bringing any place 
to the brass meridian, and finding the sun's meridian 
altitude (as in the foregoing part of the problem,) the 
greatest altitudes will be in south latitude, and the 
least in the north ; contrary to what they were before. 
Thus, at London, the sun's greatest altitude will be only 
15 degrees, instead of 62 ; and its greatest altitude at 
Cape Horn will now be 57J degrees, instead of 10|, as 
at the summer solstice ; hence it appears, that the dif- 
ference between the sun's greatest and least meridian 
altitude at any place in the temperate zone, is equal to 
the breadth of the torrid zone, viz. 47 degrees, or more 
correctly 46° 56'. On the 23d of September, when the 
sun enters Libra, that is, at the time of the autumnal 
equinox, the south pole begins to be enlightened, and, 
as the sun's declination increases southward, he will 
shine farther over the south pole, and gradually increase 
in altitude at the pole ; for, at all times, his altitude at 
either pole is equal to his declination. On the 21st of 
December, the sun will have the greatest south declina- 
tion, after which his altitude at the south pole will 
gradually diminish as his declination diminishes ; and 
on the 21st of March, when the sun's declination is 
nothing, he will appear to skim along the horizon at 
the south pole, and likewise at the north pole ; the sun 
has therefore been visible at the south pole for six 
months. 



THE TERRESTRIAL GLOBE. 57 



Problem XXII. 



To place the globe in the same situation, with respect 
to the Polar Star in the heavens, as our earth is 
to the inhabitants of the equator, fyc. viz. to illustrate 
the three positions of the sphere, right, parallel 
and oblique, so as to show the comparative length 
of the longest and shortest days. 

1. For the Right Sphere. The inhabitants who 
live upon the equator have a right sphere, and the north 
polar star appears always in (or very near) the horizon. 
Place the two poles of the globe in the horizon, then 
the north pole will correspond with the north polar star, 
and all the heavenly bodies will appear to revolve round 
the earth from east to w r est, in circles parallel to the 
equinoctial, according to their different declinations : 
one half of the starry heavens will be constantly above 
the horizon, and the other half below, so that the stars- 
will be visible for twelve hours, and invisible for the 
same space of time ; and, in the course of 6 months, an 
inhabitant upon the equator may see all the stars in the 
heavens. The ecliptic being drawn on the terrestrial 
globe, young students are often led to imagine that the 
sun apparently moves daily round the earth in the same 
oblique manner. To correct this false idea, we must 
suppose the ecliptic to be transferred to the heavens, 
where it properly points out the sun's apparent annual 
path amongst the fixed stars. The sun's diurnal path 
is either over the equator, as at the time of the equi- 
noxes, or in lines nearly parallel to the equator ; this 
may be correctly illustrated by fastening one end of a 



58 PROBLEMS PERFORMED WITH 

piece of packthread upon the point Aries on the equa- 
tor, and winding the packthread round the globe towards 
the right hand, so that one fold may touch another, till 
you come to the tropic of Cancer : thus you will have 
a correct view of the sun's apparent diurnal path from 
the vernal equinox to the summer solstice ; for, after 
a diurnal revolution, the sun does not come to the same 
point of the parallel whence it departed, but, according 
as it approaches to or recedes from the tropic, is a little 
above or below that point. When the sun is in the 
equinoctial, he will be vertical to all the inhabitants 
upon the equator, and his apparent diurnal path will 
be over that line : when the sun has ten degrees of 
north declination, his apparent diurnal path will be 
from east to west nearly along that parallel. When the 
sun has arrived at the tropic of Cancer, his diurnal path 
in the heavens will be along that line, and he will be 
vertical to all the inhabitants on the earth in latitude 23° 
28 f north. The inhabitants upon the equator will always 
have twelve hours day and twelve hours night, notwith- 
standing the variation of the sun's declination from north 
to south, or from south to north ; because the parallel of 
latitude which the sun apparently describes for any day, 
will always be cut into two equal parts by the horizon. 
The greatest meridian altitude of the sun will be 90°, 
and the least 66° 32'. During one half of the year, an 
inhabitant on the equator will see the sun full north at 
noon, and during the other half it will be full south. 

2. For the Parallel Sphere. The inhabitants, 
(if any) who live at the north pole have a parallel sphere, 
and the north polar star in the heavens appears exactly 



THE TERRESTRIAL GLOBE. 59 

(or very nearly) over their heads. Elevate the north 
pole ninety degrees above the horizon, then the equa- 
tor will coincide with the horizon, and all the parallels 
of latitude will be parallel thereto. In the summer 
half-year, that is, from the vernal to the autumnal 
equinox, the sun will appear above the horizon, con- 
sequently the stars and planets will be invisible during 
that period. When the sun enters Aries, on the 21st 
March, he will be seen by the inhabitants of the north 
pole (if there be any inhabitants) to skim just along the 
edge of the horizon : and as he increases in declination, 
he will increase in altitude, forming a kind of spiral 
course, as before described, by wrapping a thread round 
the globe. The sun's altitude at any particular hour 
is always equal to his declination. The greatest alti- 
tude the sun can have is 23° 28', at which time he has 
arrived at the tropic of Cancer ; after which he will 
gradually decrease in altitude as his declination de- 
creases. When the sun arrives at the sign Libra, he 
will again appear to skim along the edge of the horizon, 
after which he will totally disappear, having been above 
the horizon for six months. Though the inhabitants 
at the north pole will lose sight of the sun a short time 
after the autumnal equinox, yet the twilight will con- 
tinue for nearly two months ; for the sun will not be 
18° below the horizon till he enters the 20th of Scorpio, 
as may be seen by the globe. 

After the sun has descended 18° below the horizon, 
all the stars in the northern hemisphere will become 
visible, and appear to have a diurnal revolution round 
the earth from east to west, as the sun appeared to have 



60 PROBLEMS PERFORMED WITH 

when he was above the horizon. These stars will 
never set ; and the planets, when they are in any of 
the northern signs, will be visible. The inhabitants 
under the north polar star have the moon constantly 
above their horizon during fourteen revolutions of 
the earth on its axis ; and at every full moon which 
happens from the 23d of September to the 21st of 
March, the moon is in some of the northern signs, 
and consequently visible at the north pole ; for the 
sun being below the horizon at that time, the moon 
must be above the horizon, because she is always in 
that sign which is diametrically opposite to the sun at 
the time of full moon. 

When the sun is at his greatest depression below the 
horizon, being then in Capricorn, the moon is at her 
First Quarter in Aries : Full in Cancer ; and at 
her Third Quarter in Libra : and as the beginning 
of Aries is the rising point of the ecliptic, Cancer the 
highest, and Libra the setting point, the moon rises at 
her First Quarter in Aries, is most elevated above 
the horizon, and Full in Cancer, and sets at the be- 
ginning of Libra in her Third Quarter ; having been 
visible for fourteen revolutions of the earth on its axis, 
viz. during the moon's passage from Aries to Libra. 
Thus the north pole is supplied one half of the winter 
time with constant moonlight in the sun's absence ; 
and the inhabitants only lose sight of the moon from 
her Third to her First Quarter, while she gives but 
little light, and can be of little or no service to them. 

3. For the Oblique Sphere. Whenever the ter- 
restrial globe is placed in a proper situation with res- 



THE TERRESTRIAL GLOBE. 61 

pect to the fixed stars, the pole must be elevated as 
many degrees above the horizon as are equal to the 
latitude of the given place, and the north pole of the 
globe must point to the north polar star in the heavens ; 
for in sailing, or travelling from the equator northward, 
the north polar star appears to rise higher and higher. 
On the equator it will appear in the horizon ; in 10 de- 
grees of north latitude it will be ten degrees above the 
horizon ; in twenty degrees of north latitude it will be 
twenty degrees above the horizon ; and so on, always 
increasing in altitude as the latitude increases. Every 
inhabitant of the earth, except those who live upon the 
equator, or exactly under the north polar star, has an 
oblique sphere, viz. the equator cuts the horizon 
obliquely. By elevating and depressing the poles, in 
several problems, a young student is sometimes led to 
imagine that the earth's axis moves northward and south- 
ward just as the pole is raised or depressed : this is a 
mistake, the earth's axis has no such motion.* In tra- 
velling from the equator northward, our horizon varies ; 
thus, when we are on the equator, the northern point 
of our horizon is in a line with the north polar star; 
when we have travelled to ten degrees north latitude, 
the north point of our horizon is ten degrees below the 
pole, and so on : now, the wooden horizon on the ter- 
restrial globe is immovable, otherwise it ought to be 
elevated or depressed, and not the pole ; but whether 
we elevate the pole ten degrees above the horizon, or 
depress the north point of the horizon ten degrees 

*The earth's axis has a kind oflibrating motion, called the nutation, 
but this cannot be represented by elevating or depressing the pole. 

f s 



62 PROBLEMS PERFORMED WITH 

below the pole, the appearance will be exactly the 
same. 

The latitude of London is about 51i° north ; if Lon- 
don be brought to the brass meridian, and the north pole 
be elevated 51^° above the north point of the wooden 
horizon, then the wooden horizon will be the true 
horizon of London; and, if the artificial globe be 
placed exactly north and south by a mariner's compass, 
or by a meridian line, it will have exactly the position 
which the real globe has. Now, if we imagine lines 
to be drawn through every degree within the torrid zone, 
parallel to the equator, they will nearly represent the 
sun's diurnal path on any given day. By comparing 
these diurnal paths with each other, they will be found 
to increase in length from the equator northward, and 
to decrease in length from the equator southward ; 
consequently, when the sun is going north from the 
equator, the days are increasing in length to us ; and 
when going from the equator, the days are decreas- 
ing. The sun's meridian altitude, for any day, may be 
found by counting the number of degrees from the 
parallel in which the sun is on that day, towards the 
horizon, upon the brass meridian ; thus, when the sun 
is in that parallel of latitude which is ten degrees north 
of the equator, his meridian altitude will be 48£°. 
Though the wooden horizon be the true horizon of the 
given place, yet it does not separate the enlightened 
hemisphere of the globe from the dark hemisphere, 
when the pole is thus elevated. For instance, when the 
sun is in Aries, and London at the meridian, all the places 
on the globe above the horizon beyond those meridians 



THE TERRESTRIAL GLOBE. 63 

which pass through the east and west points thereof, 
reckoning towards the north, are in darkness, notwith- 
standing they are above the horizon : and all places 
below the horizon, between those same meridians and 
the southern point of the horizon, have day-light, not- 
withstanding they are below the horizon of London. 

Problem XXIII. 

The month and day of the month being given, to find all 
places of the earth where the sun is vertical on that 
day ; those places where the sun does not set, and 
those places where he does not rise on the given day. 

Rule. Find the sun's declination (by Problem XX.) 
for the given day, and mark it on the brass meridian; 
turn the globe round on its axis from west to east, and 
all the places which pass under this mark will have the 
sun vertical on that day. 

Secondly. Elevate the north or south pole, accord- 
ing as the sun's declination is north or south, so many 
degrees above the horizon as are equal to the sun's de- 
clination : turn the globe on its axis from west to east; 
then, to those places which do not descend below the 
horizon, in that frigid zone near the elevated pole, the 
sun does not set on the given day : and to those places 
which do not ascend above the horizon, in that frigid 
zone adjoining to the depressed pole, the sun does not 
rise on the given day. 

Or, by the analemma. 

Bring the analemma to that part of the brass meri- 
dian which is numbered from the equator towards the 



64 PROBLEMS PERFORMED WITH 

poles, the degree directly above the day of the month, 
on the brass meridian, is the sun's declination. Ele- 
vate the north or south pole, according as the sun's de- 
clination is north or south, so many degrees above the 
horizon as are equal to the sun's declination ; turn the 
globe on its axis from west to east, then to those places 
which pass under the sun's declination, on the brass 
meridian the sun will be vertical ; to those places (in 
that frigid zone near the elevated pole) which do not 
go below the horizon, the sun does not set ; and to 
those places (in that frigid zone near the depressed 
pole) which do not come above the horizon, the sun 
does not rise on the given day. 

Examples. 1. Find all places of the earth where 
the sun is vertical on the 11th of May, those places in 
the north frigid zone where the sun does not set, and 
those places in the south frigid zone where he does not 
rise. 

Answer. The sun is vertical at St. Anthony, one of the Cape Verd 
islands, the Virgin islands, south of St. Domingo, Jamaica, Golconda, 
&c. All the places within eighteen degrees of the north pole will have 
constant day ; and those (if any) within eighteen degrees of the south 
pole will have constant night. 

2. Whether does the sun shine over the north or 
south pole on the 27th of October, to what places will 
he be vertical at noon, what inhabitants of the earth 
will have the sun below their horizon during several 
revolutions, and to what part of the globe will the sun 
never set on that day ? 

3. Find all the places of the earth where the in- 
habitants have no shadow when the sun is on their 
meridian on the first of June. 



THE TERRESTRIAL GLOBE. 65 

4. What inhabitants of the earth have their shadows 
directed to every point of the compass during a revo- 
lution of the earth on its axis on the 15th of July ? 

5. How far does the sun shine over the south pole 
on the 14th of November, what places in the north 
frigid zone are in perpetual darkness, and to what 
places is the sun vertical ? 

6. Find all places of the earth where the moon 
will be vertical on the 3d of June 1827. 

Problem XXIV. 

A place being given in the torrid zone, to find those two 
days of the year on which the sun will be vertical at 
that place. 

Rule. Bring the given place to that part of the brass 
meridian which is numbered from the equator towards 
the poles, and mark its latitude ; turn the globe on its 
axis, and observe what two points of the ecliptic pass 
under that latitude : seek those points of the ecliptic in 
the circle of signs on the horizon, and exactly against 
them, in the circle of months stand the days required. 

Or, by the analemma. 

Find the latitude of the given place (by Problem I.) 
and mark it on the brass meridian ; bring the analem- 
ma to the brass meridian, upon which, exactly under 
the latitude, will be found the two days required. 

Examples. 1. On what two days of the year will 
the sun be vertical at Madras ? 

Answer. On the 25th of April and on the 18th of August 
/2 s2 



66 PROBLEMS PERFORMED WITH 

2. On what two days of the year is the sun vertical 
at the following places ? 

OVhy'hee St. Helena Sierra Leone 

Friendly Isles Rio Janeiro Vera Cruz 

Straits of A lass Quito Manilla 

Penang Barbadoes Tinian Isle 

Trincomale Porto Bello Pelew Islands. 

Problem XXV. 

The month and the day of the month being given (at any 
place not in the frigid zones,) to find what other day 
of the year is of the same length. 

Rule. Find the sun's place in the ecliptic for the 
given day, (by Problem XX.) bring it to the brass me- 
ridian, and observe the degree above it ; turn the globe 
on its axis till some other point of the ecliptic falls un- 
der the same degree of the meridian : find this point 
of the ecliptic on the horizon, and directly against it 
you will find the day of the month required. 

This Problem may be performed by the celestial globe in the same 



manner. 



Or, by the analemma. 

Look for the given day of the month on the analem- 
ma, and adjoining to it you will find the required day 
of the month* 

Or, without a globe. 

Any two days of the year which are of the same 
length, will be an equal number of days from the longest 
or shortest day. Hence, whatever number of days the 



THE TERRESTRIAL GLOBE. 67 

given day is before the longest or shortest day, just so 
many days will the required day be after the longest or 
shortest day, et contra. 

Examples. 1. What day of the year is of the same 
length as the 25th of April ? 
Answer. The 18th of August. 

2. What day of the year is of the same length as the 
25th of May ? 

3. If the sun rise at four o'clock in the morning at 
London on the 17th of July, on what other day of the 
year will it rise at the same hour ? 

4. If the sun set at seven o'clock in the evening at 
London on the 24th of August, on what other day of 
the year will it set at the same hour ? 

5. If the sun's meridian altitude be 90° at Trinco- 
male, in the island of Ceylon, on the 12th of April, 
on what other day of the year will the meridian alti- 
tude be the same ? 

6. If the sun's meridian altitude at London on the 
25th of April be 51° 35', on what other day of the year 
will the meridian altitude be the same ? 

7. If the sun be vertical at any place on the 15th 
of April, how many days will elapse before he is verti- 
cal a second time at that place ? 

8. If the sun be vertical at any place on the 20th of 
August, how many days will elapse before he is vertical 
a second time at that place ? 



68 PROBLEMS PERFORMED WITH 



Problem XXVI. 

The month, day, and hour of the day being given, to find 
where the sun is vertical at that instant. 

Rule. Find the sun's declination (by Problem XX.) 
and mark it on the brass meridian ; bring the given 
place to the brass meridian, and set the index of the 
hour-circle to twelve ; then, if the given time be before 
noon, turn the globe westward as many hours as it 
wants of noon ; but, if the given time be past noon, 
turn the globe eastward as many hours as the time is 
past noon ; the place exactly under the degree of the 
sun's declination will be that sought. 

Examples. 1. When it is forty minutes past six 
o'clock in the morning at London on the 25th of April, 
where is the sun vertical? 

Answer. Here the given time is five hours twenty minutes before 
noon ; hence the globe must be turned towards the west till the index 
has passed over five hours twenty minutes, and under the sun's decli- 
nation on the brass meridian you will find Madras, the place required. 

2. "When it is four o'clock in the afternoon at Lon- 
don on the 18th of August, where is the sun vertical? 

Answer. Here the given time is four hours past noon; hence the 
globe must be turned towards the east, till the index has passed 
over four hours, then, under the sun's declination, you will find Bar- 
badoes, the place required. 

3. When it is three o'clock in the afternoon at Lon- 
don on the 4th of January, where is the sun vertical? 

4. When it is three o'clock in the morning at London 
on the 11th of April, where is the sun vertical? 

5. When it is thirty-seven minutes past one o'clock 



THE TERRESTRIAL GLOBE. 69 

in the afternoon at the Cape of Good Hope on the 5th 
of February, where is the sun vertical ? 

6. When it is eleven minutes past one o'clock in the 
afternoon at London on the 29th of April, where is the 
sun vertical ? 

7. When it is twenty minutes past five o'clock in the 
afternoon at Philadelphia on the 18th of May, where is 
the sun vertical ? 

8. When it is nine o'clock in the morning at Cal- 
cutta on the 11th of April, where is the sun vertical? 

Problem XXVlI. 

The month, day, and hour of the day at any place being 
given, to find all those places of the earth where the 
sun is rising, those places where the sun is setting, 
those places that have noon, that particular place 
where the sun is vertical, those places that have morn- 
ing twilight, those places that have evening twilight, 
and those places that have midnight. 

Rule. Find the sun's declination (by Problem XX.) 
and mark it on the brass meridian ,* elevate the north 
or south pole, according as the sun's declination is 
north or south, so many degrees above the horizon as 
are equal to the sun's declination ; bring the given place 
to the brass meridian, and set the index of the hour- 
circle to twelve ; then, if the given time be before noon, 
turn the globe westward as many hours as it wants ot 
noon; but, if the given time be past noon, turn the 
globe eastward as many hours as the time is past noon : 
keep the globe in this position ,' then all places along 
the western edge of the horizon have the sun rising ; 



70 PROBLEMS PERFORMED WITH 

those places along the eastern edge have the sun set- 
ting ; those under the brass meridian above the hori- 
zon, have noon ; that particular place which stands 
under the sun's declination on the brass meridian, has 
the sun vertical; all places below the western edge of 
the horizon, within eighteen degrees, have morning 
twilight ; those places which are below the eastern 
edge of the horizon, within eighteen degrees, have 
evening twilight ; all places under the brass meridian 
below the horizon, have midnight ; all the places above 
the horizon have day, and those below it have night or 
twilight. 

Examples. 1. When it is fifty-two minutes past four 
o'clock in the morning at London on the fifth of March, 
find all places of the earth where the sun is rising, set- 
ting, &c. &c. 

Answer. The sun's declination will be found to be 6£° south ; there- 
fore, elevate the south pole 6i° above the horizon. The given time be- 
ing seven hours eight minutes before noon ( = 12 h. — 4 h. 52 m.) the 
globe must be turned towards the west, till the index has passed over 
seven hours eight minutes. Let the globe be fixed in this position ; 
then, 

The sun is rising at the western part of the White Sea, Petersburgh, 
the Morea in Turkey, &c. 

Setting at the eastern coast of Kamtschatka, Jesus island, Palmerston 
island, &c. between the Friendly and Society islands. 

Noon at the lake Baikal inlrkoutsk, Cochin China, Cambodia, Sunda 
islands, &c. 

Vertical at Batavia. 

Morning twilight at Sweden, part of Germany, the southern part of 
Italy, Sicily, the western coast of Africa along the ^Ethiopian Ocean 
&c. 

Evening twilight at the north-west extremity of North America, the 
Sandwich islands, Society islands, &c. 

Midnight at Labrador, New- York, western part of St Domingo, Chili, 
and the western coast of South America. 



THE TERRESTRIAL GLOBE. 71 

Day at the eastern part of Russia in Europe, Turkey Egypt, the Cape 
of Good Hope, and all the eastern part of Africa, almost the whole of 
Asia, &c. 

Night at the whole of North and South America, the western part of 
Africa, the British isles, Erance, Spain, Portugal, &c. 

2. When it is four o'clock in the afternoon at Lon- 
don on the 25th of April, where is the sun rising, set- 
ting, &c. &c. ? 

Answer. The sun's declination being 13° north, the north pole must 
be elevated 13° above the horizon; and as the given time is four o'clock 
in the afternoon, the globe must be turned four hours towards the east ; 
then the sun will be rising at O'why'hee, &c. setting at the Cape of 
Good Hope, &c. ; it will be noon at Buenos Ayres, &c. the sun will be 
vertical at Barbadoes, and following the directions in the Problem, all 
the other places are readily found. 

3. When it is ten o'clock in the morning at London 
on the longest day, to what countries is the sun rising, 
setting, &c. &c. ? 

4. When it is ten o'clock in the afternoon at Botany 
Bay on the 15th of October, where is the sun rising, 
setting, &c. &.c. ? 

5. When it is seven o'clock in the morning at Wash- 
ington on the 17th of February, where is the sun rising, 
setting, &c. &c. ? 

6. When it is midnight at the Cape of Good Hope 
on the 27th of July, where is the sun rising, setting, 
&c. &c. ? 

Problem XXVIII. 
To find the time of the surfs rising, and setting, and 

length of the day and night, at any place not in the 

frigid zones. 

Rule. Find the sun's declination (by Problem XX.) 
and elevate the north or south pole, according as the 



72 PROBLEMS PERFORMED WITH 

declination is north or south, so many degrees above 
the horizon as are equal to the sun's declination; bring 
the given place to the brass meridian, and set the in- 
dex of the hour-circle to twelve ; turn the globe east- 
ward till the given place comes to the eastern semi- 
circle of the horizon, and the number of hours passed 
over by the index will be the time of the sun's setting : 
deduct these hours from twelve, and you have the time 
of the sun's rising ; because the sun rises as many 
hours before twelve as it sets after twelve. Double 
the time of the sun's setting gives the length of the 
day, and double the time of rising gives the length of 
the night. 

By the same rule, the length of the longest day, at all places not in 
the frigid zones, may be readily found ; for the longest day at all places 
in north latitude is on the 21st of June, or when the sun enters Cancer ; 
and the longest day at all places in south latitude is on the 21st of De- 
cember, or when the sun enters the sign Capricorn. 

Or, 
Find the latitude of the given place, and elevate the 
north or south pole, according as the latitude is north 
or south, so many degrees above the horizon as are equal 
to the latitude ; find the sun's place in the ecliptic (by 
Problem XX.) bring it to the brass meridian, and set 
the index of the hour circle to twelve ; turn the globe 
westward till the sun's place come to the western 
semicircle of the horizon, and the number of hours 
passed over by the index will be the time of the sun's 
setting ; and these hours taken from twelve will give 
the time of rising ; then, as before, double the time of 
setting gives the length of the day, and double the time 
of rising gives the length of the night. 



TIIE TERRESTRIAL GLOBE. 73 

Or, Br THE ANALEMMA. 

Find the latitude of the given place, and elevate the 
north or south pole, according as the latitude is north 
or south, the same number of degrees above the hori- 
zon ; bring the middle of the analemma to the brass 
meridian, and set the index of the hour-circle to twelve ; 
turn the globe westward till the day of the month on 
the analemma comes to the western semicircle of the 
horizon, and the number of hours passed over by the in- 
dex will be the time of the sun's setting, &c. as above. 

Examples. 1. What time does the sun rise and set 

at London on the 1st of June, and what is the length 

of the day and night ? 

Answer. The sun sets at 8 min. past 8, and rises at 52 min.<past 3, 
the length of the day is 16 hours 16 minutes, and the length of the night 
7 hours 44 minutes. The learner will readily perceive that if the time 
at which the sun rises be given, the time at which it sets, together with 
the length of the day and night, may be found without a globe ; if the 
length of the day be given, the length of the night and the time the sun 
rises and sets may be found ; if the length of the night be given, the 
length of the day and the time the sun rises and sets are easily known. 

2. At what time does the sun rise and set at the 
following places, on the respective days mentioned, and 
what is the length of the day and night ? 



London, 17th of May 
Gibraltar, 22d July 
Edinburgh, 29th January 
Botany Bay, 20th Febru- 
ary 
Pekin, 20th April 



Cape of Good Hope, 7th 

December 
Cape Horn, 29th January 
Washington, 15th Decern. 
Petersburgh, 24th October 
Constantinople, 18th Aug. 



3. Find the time the sun rises and sets at every 
place on the surface of the globe on the 21st of March, 
and likewise on the 23d of September. 
g T 



74 PROBLEMS PERFORMED WITH 

4. Required the length of the longest day and short- 
est night at the following places : 

London Paris Pekin 

Petersburg Vienna Cape Horn 

Aberdeen Berlin Washington 

Dublin Buenos Ayres Cape of Good Hope 

Glasgow Botany Bay Copenhagen. 

5. Required the length of the shortest day and longest 
night at the following places : 

London Lima Paris 

Archangel Mexico O'why'hee 

O Taheitee St. Helena Lisbon 
Quebec Alexandria Falkland islands. 

6. How much longer is the 21st of June at Peters- 
burg than at Alexandria ? 

7. How much longer is the 21st of December at 
Alexandria than at Petersburgh ? 

8. At what time does the sun rise and set at Spitz- 
bergen on the 5th of April. ' 

Problem XXIX. 

The length of the day at any place, not in the frigid 
zones, being given, to find the surfs declination and 
the day of the month. 

Rule. Bring the given place to the brass meridian 
and set the index to twelve : turn the globe eastward 
till the index has passed over as many hours as are 
equal to half the length of the day ; keep the globe 
from revolving on its axis, and elevate or depress one 
of the poles till the given place exactly coincides with 
the eastern semicircle of the horizon ; the distance of 



THE TERRESTRIAL GLOBE. 75 

the elevated pole from the horizon will be the sun's 
declination : mark the sun's declination, thus found, 
on the brass meridian : turn the globe on its axis, and 
observe what two points of the ecliptic pass under this 
mark; seek those points in the circle of signs on 
the horizon, and exactly against them, in the circle of 
months, stand the days of the months required. 

Or, 

Bring the meridian passing through Libra to coincide 
with the brass meridian, elevate the pole to the latitude 
of the place, and set the index of the hour-circle to 
twelve ; turn the globe eastward till the index has 
passed over as many hours as are equal to half the 
length of the day, and mark where the meridian pass- 
ing through Libra is cut by the eastern semicircle of 
the horizon ; bring this mark to the brass meridian, and 
the degree above it is the sun's declination ; with which 
proceed as above. 

Or, by the analemma. 

Bring the middle of the analemma to the brass meri- 
dian, elevate the pole to the latitude of the place, and 
set the index of the hour-circle to twelve ; turn the 
globe eastward till the index has passed over as many 
hours as are equal to half the length of the day ; the 
two days, on the analemma, which are cut by the east- 
ern semicircle of the horizon, will be the days required ; 
and, by bringing the analemma to the brass meridian, 
the sun's declination will stand exactly above these 
days^ 



76 PROBLEMS PERFORMED WITH 

Examples. 1. What two days in the year are each 

sixteen hours long at London, and what is the sun's 

declination ? 

Answer. The 24th of May and the 17th of July. The sun's declina- 
tion is about 21° north. 

2. What two days of the year are each fourteen hours 
long at London ? 

3. On what two days of the year does the sun set at 
half-past seven o'clock at Edinburgh ? 

4. On what two days of the year does the sun rise 
at four o'clock at Petersburg ? 

5. What two nights of the year are each ten hours 
long at Copenhagen ? 

6. What day of the year at London is sixteen hours 
and a half long ? 

Problem XXX. 

To find the length of the longest day at any place in 
the north frigid zone. 

Rule. Bring the given place to the northern point 
of the horizon (by elevating or depressing the pole,) 
and observe its distance from the north pole on the brass 
meridian ; count the same number of degrees on the 
brass meridian from the equator, towards the north pole, 
and mark the place where the reckoning ends ; turn 
the globe on its axis, and observe what two points of 
the ecliptic pass under the above mark ; find those 
points of the ecliptic in the circle of signs on the hori- 
zon, and exactly against them, in the circle of months, 
you will find the days on which the longest day begins 
and ends. The day preceding the 21st of June is 



THE TERRESTRIAL GLOBE. 77 

that on which the longest day begins at the given place, 
and the day following the 21st of June is that on which 
the longest day ends : the time between these days is 
the length of the longest day. 

Or, by the analemma. 

Bring the given place to that part of the brass meri- 
dian which is numbered from the north pole towards 
the equator, and observe its distance in degrees from 
the pole ; count the same number of degrees on the 
br^ass meridian from the equator towards the north pole, 
and mark where the reckoning ends ; bring the ana- 
lemma to the brass meridian, and the two days which 
stand under the above mark will point out the begin- 
ning and end of the longest day. 

Examples. 1. What is the length of the longest 
day at the North Cape, in the island of Maggeroe, in 
latitude 71° 30' north? 

Answer. The place is 18£° from the pole ; the longest day begins 
on the 14th of May, and ends on the 30th of July ; the day is therefore 
seventy-seven days long, that is, the sun does not set during seventy- 
seven revolutions of the earth on its axis. 

2. What is the length of the longest day in the 
north of Spitzbergen, and on what days does it begin 
and end ? 

3. What is the length of the longest day at the 
northern extremity of Nova Zembla ? 

4. What is the length of the longest day at the north 
pole, and on what days does it begin and end? 

g 2 t 2 



78 PROBLEMS PERFORMED WITH 

Problem XXXI. 

To find the length of the longest night at any place in 
the north frigid zone. 

Rule. Bring the given place to the northern point 
of the horizon (by elevating or depressing the pole,) 
and observe its distance from the north pole on the brass 
meridian ; count the same number of degrees on the 
brass meridian from the equator towards the south pole, 
and mark the place where the reckoning ends ; turn 
the globe on its axis, and observe what two points of 
the ecliptic pass under the above mark ; find those 
points of the ecliptic in the circle of signs on the hori- 
zon, and exactly against them in the circle of months, 
you will find the days on which the longest night be- 
gins and ends. The day preceding the 21st of De- 
cember is that on which the longest night begins at the 
given place, and the day following the 21st of Decem- 
ber is that on which the longest night ends : the time 
between these days is the length of the longest night. 

Or, by the analemma. 

Bring the given place to that part of the brass meri- 
dian which is numbered from the north pole towards 
the equator, and observe its distance in degrees from 
the pole ; count the same number of degrees on the 
brass meridian from the equator towards the south pole, 
and mark where the reckoning ends ; bring the ana- 
lemma to the brass meridian, and the two days which 
stand under the above mark will point out the begin- 
ning and end of the longest night. 



TIIE TERRESTRIAL GLOBE. 79 

Examples. 1. What is the length of the longest 

night at the North Cape, in the island of Maggeroe, in 

latitude 71° 'Si)' north ? 

Answer. The place is 18£° from the pole ; the longest night begins 
on the 16lh of November, and ends on the 27th of January : the night 
is therefore seventy-three days long, that is, the sun does not rise during 
seventy-three revolutions of the earth on its axis. 

2. What is the length of the longest night at the 
north of Spitzbergen ? 

3. The Dutch wintered in Nova Zembla, latitude 76 
degrees north, in the year 1596 ; on what day of the 
month did they lose sight of the sun ; on what day of 
the month did he appear again ; and how many days 
were they deprived of his appearance, setting aside the 
effect of refraction ? 

4. For how many days are the inhabitants of the 
northernmost extremity of Russia deprived of a sight 
of the sun ? 

Problem XXXII. 

To find, the number of days which the sunrises and sets 
at any place in the north * frigid zone. 

Rule. Bring the given place to the northern point 
of the horizon, (by elevating or depressing the pole,) 
and observe its distance from the north pole on the 
brass meridian ; count the same number of degrees on 
the brass meridian from the equator towards the poles 
northward and southward, and make marks where the 
reckoning ends ; observe what two points of the eclip- 

* The same might bo found for a place in the south frigid zone, were 
that zone inhabited. 



80 PROBLEMS PERFORMED WITH 

tic nearest to Aries pass under the above marks ; these 
points will show (upon the horizon) the end of the lon- 
gest night and the beginning of the longest day ; dur- 
ing the time between these days the sun will rise and 
set every twenty-four hours ; next observe what two 
points of the ecliptic, nearest to Libra, pass under the 
marks on the brass meridian ; find these points, as be- 
fore, in the circle of signs, and against them you will 
find the day on which the longest day ends at the given 
place, and the day on which the longest night begins ; 
during the time between these days the sun will rise 
and set every twenty -four hours. 

Or, 

Find the length of tl>e longest day at the given place 
(by Prob. XXX.) and the length of the longest night 
(by Prob. XXXI.) add these together, and subtract the 
sum from 365 days, the length of the year, the remain- 
der will show the number of days which the sun rises 
and sets at that place. 

Or, BY THE ANALEMMA. 

Find how many degrees the given place is from the 
north pole, and mark those degrees upon the brass 
meridian on both sides of the equator ; observe what 
four days on the analemma stand under the marks on 
the brass meridian ; the time between those two days 
on the left hand part of the analemma (reckoning to- 
wards the north pole) will be the number of days on 
which the sun rises and sets, between the end of the 
longest night and the beginning of the longest day : 



THE TERRESTRIAL GLOBE. 81 

and the lime between the two days on the right-hand 

part of the analemma (reckoning towards the south 

pole) will be the number of days on which the sun rises 

and sets, between the end of the longest day and the 

beginning of the longest night. 

Examples. 1. How many days in the year does the 

sun rise and set at the North Cape, in the island of 

Maggeroe, in latitude 71° 30' north? 

Answer. The place is 18|° from the pole, the two points in the 
ecliptic, nearest to Aries, which pass under 18£° on the brass meridian, 
are 8° in *%,, answering to the 27th of January, and 24° in &, answering 
to the 14th of May. Hence the sun rises and sets for 107 days, viz. 
from the end of the longest night, which happens on the 27th of Janu- 
ary, to the beginning of the longest day, which happens on the 14th of 
May. Secondly, the two points in the ecliptic, nearest to Libra, which 
pass under 18£° on the brass meridian, are 8 C in Q. answering to the 
30lh of July, and 24° in Ttj , answering to the 15th of November. Hence 
the sun rises and sets for 108 daj^s, viz. from the end of the longest 
day, which happens on the 30th of July, to the beginning of the longest 
night, which happens on the 15th of November ; so that the whole 
time of the sun's rising and setting is 215 days. 

Or, thus : 

The length of the longest day, by Example 1st, Prob. XXX. is 77 
days ; the length of the longest night by Example 1st, Prob. XXXI. is 
73 days ; the sum of these is 150, which, deducted from 365, leaves 215 
days as above. 

2. How many days in the year does the sun rise and 
set at the north of Spitzbergen ? 

3. How many days does the sun rise and set at Green- 
land, in latitude 75° north ? 

4. How many days does the sun rise and set at the 
northern extremity of Russia in Asia? 



82 PROBLEMS PERFORMED WITH 

Problem XXXIII. 

To find in what degree of north latitude, on any day 
between the 21st of March and the 21st of June , or 
in what degree of south latitude, on any day between 
the 23d of September and the 21st of December, the 
sun begins to shine constantly without setting ; and 
also in what latitude in the opposite hemisphere he 
begins to be totally absent. 

Rule. Find the sun's declination (by Prob. XX.) 
and count the same number of degrees from the north 
pole towards the equator, if the declination be north, 
or from the south pole, if it be south, and mark the 
point where the reckoning ends ; turn the globe on its 
axis, and all places passing under this mark are those 
in which the sun begins to shine constantly without 
setting at that time : the same number of degrees from 
the contrary pole will point out all the places where 
twilight or total darkness begins. 

Examples. 1. In what latitude north, and at what 
places, does the sun begin to shine without setting dur- 
ing several revolutions of the earth on its axis, on the 
14th of May? 

Answer. The sun's declination is 18£° north, therefore all places in 
latitude 71 £° north will be the places sought, viz. the North Cape in 
Lapland, the southern part of Nova Zembla, Icy Cape, &c. 

2. In what latitude south does the sun begin to shine 
without setting on the 18th of October, and in what 
latitude north does he begin to be totally absent ? 

Answer. The sun's declination is 10° south, therefore he begins to 
shine constantly in latitude 80° south, where there are no inhabitants 



THE TERRESTRIAL GLOBE. 83 

known, and to be totally absent in latitude 80° north, viz. at Spits- 
bergen. 

3. In what latitude does the sun begin to shine with- 
out setting on the 20th of April ? 

4. In what latitude north does the sun begin to shine 
without setting on the 1st of June, and in what degree 
of south latitude does he begin to be totally absent? 

Problem XXXIV. 

Any number of days, not exceeding 186, being given, 

to find the parallel of north latitude in which the sun 

does not set for that time. 

Rule. Count half the number of days from the 21st 
of June on the horizon, eastward or westward, and op- 
posite to the last day you will find the sun's place in 
the circle of signs : look for the sign and degree on the 
ecliptic, which bring to the brass meridian, and observe 
the sun's declination ; reckon the same number of de- 
grees from the north pole (on that part of the brass me- 
ridian which is numbered from the equator towards 
the poles) and you will have the latitude sought. 

Examples. 1. In what degree of north latitude, 

and at what places, does the sun continue above the 

horizon for seventy-seven days'? 

Answer. Half the number of days is 38£, and if reckoned backward 
or towards the east, from the 21st of June, will answer to the 14th of 
May ; and if counted forward, or towards the west, will answer to the 
30th of July ; on either of which days the sun's declination is 18| de- 
grees north, consequently the places sought are 18£ degrees from the 
north pole, or in latitude 71| degrees north ; answering to the North 
Cape in Lapland, the south part of Nova Zembla, Icy Cape, &c. 

2. In what degree of north latitude is the longest 
day 134 days, or 3216 hours in length ? 



84 PROBLEMS PERFORMED WITH 

3. In what degree of north latitude does the sun 
continue above the horizon for 2160 hours? 

4. In what degree of north latitude does the sun con- 
tinue above the horizon for 1152 hours? 

Problem XXXV. 

To find the beginning, end, and duration of twilight at 
any given 'place on any given day. 

Rule. Find the sun's declination for the given day 
(by Problem XX.) and elevate the north or south pole, 
according as the declination is north or south, so many 
degrees above the horizon as are equal to the sun's de- 
clination ; screw the quadrant of altitude on the brass 
meridian, over the degree of the sun's declination ; 
bring the given place to the brass meridian, and set the 
index of the hour-circle to twelve : turn the globe east- 
ward till the given place comes to the horizon, and the 
hours passed over by the index will show the time of 
the sun's setting, or the beginning of evening twilight : 
continue the motion of the globe eastward, till the given 
place coincides with 18° on the quadrant of altitude 
below the horizon, and the hours passed over by the 
index, from 12, will show T when evening twilight ends. 
The time when evening twilight ends, subtracted from 
12, will show the beginning of morning twilight. 

Or, thus : 

Elevate the north or south pole, according as the la- 
titude of the given place is north or south, so many 
degrees above the horizon as are equal to the latitude ; 
find the sun's place in the ecliptic, bring it to the brass 



THE TERRESTRIAL GLOBE. 85 

meridian, set the index of the hour-circle to twelve, 
and screw the quadrant of altitude upon the brass me- 
ridian over the given latitude : turn the globe westward 
on its axis till the sun's place comes to the western 
edge of the horizon, and the hours passed over by the 
index will show the time of the sun's setting, or the 
beginning of evening twilight ; continue the motion of 
the globe westward till the sun's place coincides with 
18° on the quadrant of altitude below the horizon, the 
time passed over by the index of the hour-circle, from 
the time of the sun's setting, will show the duration of 
evening twilight. 

Or, by the analemma. 

Elevate the pole to the latitude of the place, as above, 
and screw the quadrant of altitude upon the brass me- 
ridian over the degree of latitude ; bring the middle 
of the analemma to the brass meridian, and set the in- 
dex of the hour-circle to twelve ; turn the globe west- 
ward till the given day of the month, on the analemma, 
comes to the western edge of the horizon, and the 
hours passed over by the index will show the time of 
the sun's setting, or the beginning of evening twilight : 
continue the motion of the globe westward till the 
given day of the month coincides with 18° on the 
quadrant below the horizon, the time passed over by 
the index, from the time of the sun's setting, will show 
the duration of evening twilight. 

Examples. 1. Required the beginning, end, and 
duration of morning and evening twilight at London on 
the 19th of April? 

h U 



86 PROBLEMS PERFORMED WITH 

Answer. The sun sets at two minutes past seven, and evening twi- 
light ends at nineteen minutes past nine ; consequently morning twi- 
light begins at (12 h. —9 h. 19 m. =) 2 h. 41 m. and ends at (12 h. — 7 h 
2 m. = ) 4 h. 58 m. ; the duration of twilight is 2 h. and 17 minutes. 

2. What is the duration of twilight at London on the 

23d of September, what time does dark night begin, 

and at what time does day break in the morning? 

Answer. The sun sets at six o'clock, and the duration of twilight is 
two hours ; consequently the evening twilight ends at eight o'clock, and 
the morning twilight begins at four. 

3. Required the beginning, end, and duration of 
morning and evening twilight at London on the 25th 
of August ? 

4. Required the beginning, end, and duration of 
morning and evening twilight at Edinburgh on the 20th 
of February ? 

5. Required the beginning, end, and duration of 
morning and evening twilight at Cape Horn on the 20th 
of February ? 

6. Required the beginning, end, and duration of 
morning and evening twilight at Madras on the 15th 
of June ? 

Problem XXXVI. 

To find the beginning, end, and duration of constant 
day or ticilight at any place. 

Rule. Find the latitude of the given place, and 
add 18° to that latitude; count the number of degrees 
correspondent to the sum, on that part of the brass me- 
ridian which is numbered from the pole towards the 
equator, mark where the reckoning ends, and observe 
what two points of the ecliptic pass under the mark ; 



TIIE TERRESTRIAL GLOBE. 87 

that point wherein the sun's declination is increasing 
will show on the horizon the beginning of constant 
twilight; and that point wherein the sun's declination is 
decreasing, will show the end of constant twilight. 

Examples. 1. When do we begin to have constant 
day or twilight at London, and how long does it con- 
tinue ? 

Answer. The latitude of London is 5H degrees north, to which 
add 18 degrees, the sum is 69£, the two points of the ecliptic which pass 
under 69s are two degrees in n, answering to the 22d of May, and 29 
degrees in 05, answering to the 21st of July ; so that, from the 22d of 
May to the 21st of July the sun never descends 18 degrees below the 
horizon of London. 

2. When do the inhabitants of the Shetland islands 
cease to have constant day or twilight? 

3. Can twilight ever continue from sun-set to sun- 
rise at Madrid ? 

4. When does constant day or twilight begin at 
Spitzbergen? 

5. What is the duration of constant day or twilight 
at the North Cape in Lapland, and on what day, after 
their long winter's night, do the sun's rays first enter 
the atmosphere ? 

Problem XXXVII. 
To find the duration of twilight at the north pole. 

Rule. Elevate the north pole so that the equator 
may coincide with the horizon ; observe what point of 
the ecliptic nearest to Libra passes under 18° below 
the horizon, reckoned on the brass meridian, and find 
the day of the month correspondent thereto ; the time 
elapsed from the 23d of September to this time will be 



88 PROBLEMS PERFORMED WITH 

the duration of evening twilight. Secondly, observe 

what point of the ecliptic, nearest to Aries, passes 

under 18° below the horizon, reckoned on the brass 

meridian, and find the day of the month correspondent 

thereto ; the time elapsed from that day to the 21st of 

March will be the duration of morning twilight. 

Example. What is the duration of twilight at the 

north pole, and what is the duration of dark night 

there ? 

Answer. The point of the ecliptic nearest to Libra which passes 
under 18 degrees below the horizon, is 22 degrees in Vf[, answering to 
the 13th of November ; hence the evening twilight continues from the 
23d of September (the end of the longest day) to the 13th of Novem- 
ber, (the beginning of dark night) being 51 days. The point of the 
ecliptic nearest to Aries which passes under 18 degrees below the hori- 
zon is 9 degrees in COS, answering to the 29th of January ; hence the 
morning twilight continues from the 29th of January to the 21st of 
March (the beginning of the longest day) being 51 days. From the 23d 
of September to the 21st of March are 179 days, from which deduct 
102 ( = 51 x 2,) the remainder is 77 days, the duration of total dark- 
ness at the north pole ; but, even during this short period, the moon and 
the Aurora Borealis shine with uncommon splendour. 

Problem XXXVIII. 

To find in what climate any given place on the globe is 

situated. 

Rule. 1. If the place be not in the fngid zone, 
find the length of the longest day at that place (by 
Problem XXVIII.) and subtract twelve hours there- 
from ; the number of half hours in the remainder will 
show the climate. 

2. If the place be in the frigid zone,* find the length 

* The climates between the polar circles and the poles were un- 
known to the ancient geographers ; they reckoned only seven climates 



THE TERRESTRIAL GLOfiE. 89 

of the longest day at that place (by Problem XXX.) 
and if that be less than thirty days, the place is in the 
twenty-fifth climate, or the first within the polar circle. 
If more than thirty and less than sixty, it is in the 
twenty-sixth climate, or the second within the polar 
circle ; if more than sixty, and Jess than ninety, it is in 
the twenty-seventh climate, or the third within the 
polar circle, &c. 

Examples. 1. In what climate is London, and 
what other remarkable places are situated in the same 
climate ? 

Answer. The longest day in London is 16£ hours, if we deduct 12 
therefrom, the remainder will be 4£ hours, or nine half hours ; hence 
London is in the ninth climate north of the equator; and as all places 
in or near the same latitude are in the same climate, we shall find 
Amsterdam, Dresden, Warsaw, Irkoutsk, the southern part of the pe- 
ninsula of Kamtschatka, Nootka Sound, the south of Hudson's Bay, the 
north of .Newfoundland, &c. to be in the same climate as London. 

2. In what climate is the North Cape in the island 
of Maggeroe, latitude 71° 30' north? 

north of the equator. The middle of the first northern climate they 
made to pass through Meroe, a city of Ethiopia, built by Cambyses on 
an island in the Nile, nearly under the tropic of Cancer ; the second 
through Syene, a city of Thebais in Upper Egypt, near the cataracts of 
the Nile ; the third through Alexandria ; the fourth through Rhodes ; 
the fifth through Rome or the Hellespont ; the sixth throi*gh the mouth 
of the Borysthenes or Dnieper ; and the seventh through the Riphhcean 
mountains, supposed to be situated near the source of the Tanais or Don 
river. The southern parts of the earth being in a great measure un- 
known, the climates received their names from the northern ones, 
and not from particular towns or places. Thus the climate, which 
w r as supposed to be at the same distance from the equator southward 
as Meroe was northward, was called Antidiameroes, or the opposite 
climate to Meroe ; Antidiasyenes was the opposite climate to Syenes, 
&c. 

h2 u2 



90 PROBLEMS PERFORMED WITH 

Answer. The length of the longest day is 77 days ; these days di- 
vided by 30, give two months for the quotient, and a remainder of 17 
days ; hence the place is in the third climate within the polar circle, or 
the 27th climate reckoning from the equator. The southern part of 
Nova Zembla, the northern part of Siberia, James' Island, Baffin's Bay, 
the northern part of Greenland, &c. are in the same climate. 

3. In what climate is Edinburgh, and what other 
places are situated in the same climate ? 

4. In what climate is the north of Spitzbergen ? 

5. In what climate is Cape Horn ? 

6. In what climate is Botany Bay, and what other 
places are situated in the same climate ? 

Problem XXXIX. 

To find the breadths of the several climates between the 
equator and the polar circles. 

Rule. For the northern climates. Elevate the north 
pole 23i° above the northern point of the horizon ; 
bring the sign Cancer to the meridian, and set the in- 
dex to twelve ; turn the globe eastward on its axis till 
the index has passed over a quarter of an hour ; observe 
that particular point of the meridian passing through 
Libra, which is cut by the horizon, and at the point of 
intersection make a mark with a pencil ; continue the 
motion of the globe eastward till the index has passed 
over another quarter of an hour, and make a second 
mark : proceed thus till the meridian passing through 
Libra* will no longer cut the horizon ; the several 

* On Adams' and Cary's globes, the meridian passing through Libra 
is divided into degrees, in the same manner as the brass meridian is di- 
vided ; the horizon will, therefore, cut this meridian in the several de- 
grees answering to the end of each climate, without the trouble of bring- 
ing it to the brass meridian, or marking the globe. 



THE TERRESTRIAL GLOBE. 91 

marks brought to the brass meridian will point out the 
latitude where each climate ends. 

Examples. 1. What is the breadth of the ninth north 
climate, and what places are situated within it ? 

Answer. The breadth of the 9th climate is 2° 57' ; it begins in lati- 
tude 49° 2' north, and ends in latitude 51° 59' north, and all places situ- 
ated within this space are in the same climate. The places will be 
nearly the same as those enumerated in the first example to the preced- 
ing problem. 

2. What is the breadth of the second climate, and 
in what latitude does it begin and end ? 

3. Required the beginning, end, and breadth of the 
fifth climate? 

4. What is the breadth of the seventh climate north 
of the equator, in what latitude does it begin and end, 
and what places are situated within it ? 

5. What is the breadth of the climate in which Pe- 
tersburg is situated ? 

6. What is the breadth of the climate in which 
Mount Heckla is situated ? 

Problem XL. 

To find that part of the equation of time which depends 
on the obliquity of the ecliptic. 

Rule. Find the sun's place in the ecliptic, and bring 
it to the brass meridian ; count the number of degrees 
from Aries to the brass meridian, on the equator and 
on the ecliptic ; the difference, reckoning four minutes 
of time to a degree, is the equation of time. If the 
number of the degrees on the ecliptic exceed those on 
the equator, the sun is faster than the clock ; but if the 



93 



/ 



PROBLEMS PERFORMED WITH 



number of degrees on the equator exceed those on the 
ecliptic, the sun is slower than the clock. 



Note. The equation of time, or differ- 
ence between the time shown by a well- 
regulated clock, and a true sun-dial, de- 
pends upon two causes, viz. the obliquity 
of the ecliptic, and the unequal motion 
of the earth in its orbit. The former of 
these causes may be explained by the 
above Problem. If two suns were to set 
off at the same time from the point Aries, 
and move over equal spaces in equal 
time, the one on the ecliptic, the other on 
the equator, it is evident they would 
never come to the meridian together, ex- 
cept at the time of the equinoxes, and on 
the longest and shortest days. The an- 
nexed table shows how much the sun is 
faster or slower than the clock ought to 
be, so far as the variation depends on the 
obliquity of the ecliptic only. The signs 
of the first and third quadrants of the 
ecliptic are at the top of the table, and the 
degrees in these signs on the left hand ; 
in any of these signs the sun is faster than 
the clock. The signs of the second and 
third quadrants are at the bottom of the 
table, and the degrees in these signs at 
the right hand ; in any of these signs the 
sun is lower than the clock. 

Thus, w T hen the sun is in 20 degrees 
of ^ or ?T[, it is 9 minutes 50 seconds 
faster than the clock, and, when the sun 
is in 18 degrees of 05 or y$, it is 6 mi- 
nutes 2 seconds slower than the clock. 



Sun faster than the Clock in 


OB 

03 

2 


qp 


a 


n 


lQu 


Q 


»r\. 


n 


t 


3Qu 




M. S. 


M. S. 


M. S. 










8 24 


8 46 


30 


1 


20 


8 35 


8 36 


29 


2 


40 


8 45 


8 25 


28 


3 


1 


8 54 


8 14 


27 


4 


1 19|9 3 


8 1 


26 


5 


1 39 


9 11 


7 49 


25 


6 


1 59 


9 18 


7 35 


24 


7 


2 18 


9 24 


7 21 


23 


8 


2 37 


9 31 


7 6 


22 


9 


2 56 


9 36 


6 51 


21 


10 


3 16 


9 41 


6 35 


20 


11 


3 34 9 45 


6 19 


19 


12 


3 53l9 49 


6 2 


18 


13 


4 119 51 


5 45 


17 


14 


4 29 9 53 


5 27 


16 


15 


4 47 ( 9 54 


5 9 


15 


16 


5 49 55 


4 50 


14 


17 


5 21 9 55 


4 31 


13 


18 


5 38 9 54 


4 12 


12 


19 


5 54 9 52 


3 52 


11 


20 


6 10 9 50 


3 32 


10 


21 


6 26 9 47 


3 12 


9 


22 


6 41 9 43 


2 51 


8 


23 


6 35 9 38 


2 30 


7 


24 


7 9 9 33 


2 9 


6 


25 


7 23 9 27 


1 48 


5 


26 


7 36 9 20 


1 27 


4 


27 


7 49 9 13 


1 5 


3 


28 


8 19 5 


43 


2 


29 


8 13 ,8 56 


22 


1 


30 


8 2^8 46 








2Qu 


m 


a 


25 


hi 




4Qu 


X 




vs 


Q 


Sun slower than the Clock in 



THE TERRESTRIAL GLOBE. 93 

Examples. 1. What is the equation of time on the 
17th of July? 

Answer. The degrees on the equator exceed the degrees on the 
ecliptic by two ; hence the sun is eight minutes slower than the clock. 

2. On what four days of the year is the equation of 
time nothing ? 

3. What is the equation of time dependant on the 
obliquity of the ecliptic on the 27th of October? 

4. When the sun is in 18° of Aries, what is the 
equation of time ? 

Problem XLI. 

To find the surfs meridian altitude at any time of the 
year at any given place* 

Rule. Find the sun's declination, and elevate the 
pole to that declination ; bring the given place to the 
brass meridian, and count the number of degrees on 
the brass meridian (the nearest) to the horizon ; these 
degrees will show the sun's meridian altitude. 

Note. The sun's altitude may be found at any particular hour, in 
the following manner. 

Find the sun's declination, and elevate the pole to that declination ; 
bring the given place to the brass meridian and set the index to 12 ; 
then, if the given time be before noon, turn the globe westward as 
many hours as the time wants of noon ; if the given time be past noon, 
turn the globe eastward as many hours as the time is past noon. Keep 
the globe fixed in this position, and screw the quadrant of altitude on 
the brass meridian over the sun's declination ; bring the graduated 
edge of the quadrant to coincide with the given place, and the number 
of degrees between that place and the horizon will show the sun's al- 
titude. 

Or, 
Elevate the pole so many degrees above the horizon 



94 PROBLEMS PERFORMED WITH 

as are equal to the latitude of the place ; find the sun's 
place in the ecliptic, and bring it to that part of the 
brass meridian which is numbered from the equator to- 
wards the poles ; count the number of degrees con- 
tained on the brass meridian between the sun's place 
and the horizon, and they will show the altitude. 
To find the sun's altitude at any hour, see Problem XLIV. 

Or, by the analemma. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place ; find the day 
of the month on the analemma, and bring it to that part 
of the brass meridian which is numbered from the 
equator towards the poles ; count the number of degrees 
contained on the brass meridian between the given day 
of the month and the horizon, and they will show the 
altitude. 
"To find the sun's altitude at any hour, see Problem XLIV. 

Examples. 1. What is the sun's meridian altitude 
at London on the 21st of June? 

Answer. 62 degrees. 

2. What is the sun's meridian altitude at London on 
the 21st of March? 

3. What is the sun's least meridian altitude at Lon- 
don? 

4. What is the sun's greatest meridian altitude at 
Cape Horn ? 

5. What is the sun's meridian altitude at Madras on 
the 20th of June ? 

6. What is the sun's meridian altitude at Bencoolen 
©n the 15th of January ? 



THE TERRESTRIAL GLOBE. 95 

Examples to the note. 

1. What is the sun's altitude at Madrid on the 24th 
of August, at 11 o'clock in the morning? 

Answer, The sun's declination is 11^ degrees north ; by elevating 
the north pole \\~ degrees above the horizon, and turning the globe so 
that Madrid may be one hour westward of the meridian, the sun's alti- 
tude will be found to be 5?i degrees. 

2. What is the sun's altitude at London at 3 o'clock 
in the afternoon on the 25th of April ? 

3. What is the sun's altitude at Rome on the 16th 
of January at 10 o'clock in the morning? 

4. Required the sun's altitude at Buenos Ayres on 
the 21st of December at two o'clock in the afternoon? 

Problem XL1I. 

When it is midnight at any place in the temperate or 
torrid zones, to find the surfs altitude at any place 
(on the same meridian) in the north frigid zone, where 
the sun does not descend below the horizon. 

Rule. Find the sun's declination for the given day, 
and elevate the pole to that declination ,* bring the place 
(in the frigid zone) to that part of the brass meridian 
which is numbered from the north pole towards the 
equator, and the number of degrees between it and the 
horizon will be the sun's altitude. 

Or, 

Elevate the north pole so many degrees above the 
horizon as are equal to the latitude of the place in the 



96 PROBLEMS PERFORMED WITH 

frigid zone ; bring the sun's place in the ecliptic to the 
brass meridian, and set the index of the hour-circle to 
twelve ; turn the globe on its axis till the index points 
to the other twelve ; and the number of degrees be- 
tween the sun's place and the horizon, counted on the 
brass meridian towards that part of the horizon marked 
north, will be the sun's altitude. 

Examples. 1. What is the sun's altitude at the 
North Cape in Lapland, when it is midnight at Alexan- 
dria in Egypt on the 21st of June ? 

Answer. 5 degrees. 

2. When it is midnight to the inhabitants of the 
island of Sicily on the 22d of May, what is the sun's 
altitude at the north of Spitsbergen, in latitude 80° 
north ? 

3. What is the sun's altitude at the north-east of 
Nova Zembla, when it is midnight at Tobolsk, on the 
15 th of July? 

4. What is the sun's altitude at the north of Baffin's 
Bay, when it is midnight at Buenos Ayres, on the 28th 
of May ? 

Problem XLIII. 

To find the sun's amplitude at any place* 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the given place ; find the 
sun's place in the ecliptic, and bring it to the eastern 
semicircle of the horizon ; the number of degrees from 
the sun's place to the east point of the horizon will be 
the rising amplitude ; bring the sun's place to the west- 



THE TERRESTRIAL GLOBE. 97 

em semicircle of the horizon, and the number of de- 
grees from the sun's place to the west point of the hori- 
zon will be the setting amplitude. 

Or, BY THE ANALEMMA. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place ; bring the day 
of the month on the analemma to the eastern semicircle 
of the horizon : the number of degrees from the day of 
the month to the east point of the horizon will be the 
rising amplitude : bring the day of the month to the 
western semicircle of the horizon, and the number of 
degrees from the day of the month to the west point of 
the horizon will be the setting amplitude. 

Examples. 1. What is the sun's amplitude at Lon- 
don on the 21st of June? 

Answer. 39° 48' to the north of the east, and 39° 48' to the north of 
the west. 

2. On what point of the compass does the sun rise 
and set at London on the 17th of May? 

3. On what point of the compass does the sun rise 
and set at the Cape of Good Hope on the 21st of De- 
cember? 

4. On what point of the compass does the sun rise 
and set on the 21st of March? 

5. On what point of the compass does the sun rise 
and set at Washington on the 21st of October? 

6. On what point of the compass does the sun rise 
and set at Petersburg on the 18th of December? 

7. On December 22d, 1827, in latitude 31° 38' S. 
and longitude 83° W., if the sun set on the S. W. point 
of the compass, what is the variation ? 

i X 



t)8 PROBLEMS PERFORMED WITH 

8. On the 15th of May 1827, if the sun rise E. by 
N. in latitude 33° 15' N. and longitude 18° W., what 
is the variation of the compass ? 

Problem XLIV. 

To find the surfs azimuth and his altitude at any place, 
the day and hour being given* 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude on the brass meridian, 
over that latitude ; find the sun's place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour-circle to twelve ; then if the given time be before 
noon, turn the globe eastward* as many hours as it 
wants of noon ; but, if the given time be past noon, 
turn the globe westward as many hours as it is past 
noon, bring the graduated edge of the quadrant of alti- 
tude to coincide with the sun's place, then the number 
of degrees on the horizon, reckoned from the north or 
south point thereof to the graduated edge of the 
quadrant, will show the azimuth ; and the number of 
degrees on the quadrant, counting from the horizon to 
the sun's place, will be the sun's altitude. 

* Whenever the pole is elevated for the latitude of the place, the pro- 
per motion of the globe is from east to west, and the sun is on the east 
side of the brass meridian in the morning, and on the west side in the 
afternoon ; but when the pole is elevated for the sun's declination, the 
motion is from west to east, and the place is on the west side of the me- 
ridian in the morning, and on the east side in the afternoon. 



the terrestrial globe. 99 

Or, by the analemma. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place, and screw the 
quadrant of altitude on the brass meridian, over that 
latitude ; bring the middle of the analemma to the brass 
meridian, and set the index of the hour-circle to 
twelve ; then, if the given time be before noon, turn 
the globe eastward on its axis as many hours as it wants 
of noon ; but, if the given time be past noon, turn the 
globe westward as many hours as it is past noon ; bring 
the graduated edge of the quadrant of altitude to coin- 
cide with the day of the month on the analemma, then 
the number of degrees on the horizon, reckoned from 
the north or south point thereof to the graduated edge 
of the quadrant, will show the azimuth ; and the num- 
ber of degrees on the quadrant, counting from the ho- 
rizon to the day of the month, will be the sun's altitude. 

Examples. 1. What is the sun's altitude, and his 
azimuth from the north, at London, on the 1st of May, 
at ten o'clock in the morning? 

Answer. The altitude is 47°, and the azimuth from the north 136°, 
or from the south 44°. 

2. What is the sun's altitude and azimuth at Peters- 
burg on the 13th of August, at half past five o'clock 
in the morning ? 

3. What is the sun's azimuth and altitude at Anti- 
gua, on the 21st of June, at half past six in the morn- 
ing, and at half past ten ? 

4. At Barbadoes on the 21st of June, required the 
sun's azimuth and altitude at 8 minutes past 6, and at 



100 PROBLEMS PERFORMED WITH 

5 past 9 in the morning : also at i past 2, and at 52 
minutes past 5 in the afternoon. 

5. On the 13th of August at half past eight o'clock 
in the morning, at sea, in latitude 57° N. the observed 
azimuth of the sun was S. 40° 14' E., what was the 
sun's altitude, his true azimuth, and the variation of 
the compass? 

6. On the 14th of January, in latitude 33° 52' S., 
at half past three o'clock in the afternoon, the sun's 
magnetic azimuth was observed to be N. 63° 51' W. ; 
what was the true azimuth, the variation of the com- 
pass, and the sun's altitude ? 

Problem XLV. 
The latitude of the place, day of the month, and the 
surfs altitude being given, to find the surfs azimuth 
and the hour of the day. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude on the brass meridian, 
over that latitude ; bring the sun's place in the ecliptic 
to the brass meridian, and set the index of the hour- 
circle to twelve ; turn the globe on its axis till the sun's 
place in the ecliptic coincides with the given degree 
of altitude on the quadrant ; the hours passed over by 
the index of the hour-circle will show the time from 
noon, and the azimuth will be found on the horizon, 
as in the preceding problem. 

Or, by the analemma. 
Elevate the pole to the latitude of the place, and 
screw the quadrant of altitude over that latitude ; bring 



THE TERRESTRIAL GLOBE. 101 

the middle of the analemma to the brass meridian, and 
set the index of the hour-circle to twelve ; move the 
globe and the quadrant till the day of the month coin- 
cides with the given altitude, the hours passed over by 
the index will show the time from noon, and the azi- 
muth will be found in the horizon as before. 

Examples. 1. At what hour of the day on the 21st 
of March is the sun's altitude 22£° at London, and 
what is his azimuth? The observation being made in 
the afternoon. 

Answer. The time from noon will be found to be 3 hours 30 mi- 
nutes, and the azimuth 59° ]' from the south towards the west. Had 
the observations been made before noon, the time from noon would 
have been 3£ hours, viz. it would have been 30 minutes past eight in 
the morning, and the azimuth would have been 59° V from the south 
towards the east 

2. At what hour on the 9th of March is the sun's al- 
titude 25° at London, and what is his azimuth ? The 
observation being made in the forenoon. 

3. At what hour on the 18th of May is the sun's al- 
titude 30° at Lisbon, and what is the azimuth ? The 
observation being made in the afternoon. 

4. Walking along the side of Queen-square in Lon- 
don on the 5th of August in the forenoon, I observed 
the shadows of the iron -rails to be exactly the same 
length as the rails themselves ; pray what o'clock was 
it, and on what point of the compass did the shadows 
of the rails fall ? 

5. At what hour of the day on the 20th of Septem- 
ber, is the sun's altitude 21° at Quebec, and what is 
its azimuth, the observation being made in the 
morning ? 



102 PROBLEMS PERFORMED WITH 

6. At what hour on the 15th of June is the sun's al- 
titude 30° at Philadelphia, and what is the azimuth, 
the observation being made in the afternoon ? 

Problem XLVI. 

Given the latitude of the place, and the day of the month, 
to find at what hour the sun is due east or west. 

Rule. Elevate the pole so many degrees above 
the horizon as are equal to the latitude of the place, 
find the sun's place in the ecliptic, bring it to the brass 
meridian, and set the index of the hour-circle to twelve ; 
screw the quadrant of altitude on the brass meridian, 
over the given latitude, and move the lower end of it 
to the east point of the horizon ; hold the quadrant in 
this position, and move the globe on its axis till the 
sun's place comes to the graduated edge of the qua 
drant ; the hours passed over by the index from twelve 
will be the time from noon when the sun is due east, 
and at the same time from noon he will be due west. 

Examples. 1. At what hour will the sun be due 
east at London on the 19th of May ; at what hour will 
he be due west; and what will his altitude be at these 

times ? 

Answer. The time from 12 when the sun is due east, is 4 hours 54 
minutes ; hence the sun is due east at six minutes past seven o'clock in 
the morning, and due west at 54 minutes past four in the afternoon ; 
the sun's altitude will be found at the same time, as in Problem XUV. 
In this example it is 25° 26'. 

2. At what hours will the sun be due east and west 
at London on the 21st of June, and on the 21st of De- 
cember ; and what will be his altitude above the horl 
zon on the 21st of June? 



THE TERRESTRIAL GLOBE. 103 

3. Find at what hours the sun will be due east and 
west, not only at London, but at every place on the 
surface of the globe, on the 21st of March and on the 
23d of September? 

4, At what hours is the sun due east and west at 
Buenos Ayres on the 21st of December ? 

Problem XLVII. 

Given the surfs meridian altitude, and the day of the 
month, to find the latitude of the place. 

Rule. Find the sun's place in the ecliptic, and 
bring it to that part of the brass meridian which is 
numbered from the equator towards the poles ; then, 
if the sun was south of the observer when the altitude 
was taken, count the number of degrees from the sun's 
place on the brass meridian towards the south point of 
the horizon, and mark where the reckoning ends; bring 
this mark to coincide with the south point of the hori- 
zon, and the elevation of the north pole will show the 
latitude. If the sun was north of the observer when 
the altitude was taken, the degrees must be counted in 
a similar manner, from the sun's place towards the 
north point of the horizon, and the elevation, of the 
south pole will show the latitude. 

Or, without a globe. 

Subtract the sun's altitude from ninety degrees, the 
remainder is the zenith distance. If the sun be south 
when his altitude is taken, call the zenith distance 
north ; but, if north, call it south ; find the sun's de- 



104 PROBLEMS PERFORMED WITH 

clination in an ephemeris or a table of the sun's de- 
clination, and mark whether it be north or south ; then, 
if the zenith distance, and declination have the same 
name, their sum is the latitude, but, if they have con- 
trary names, their difference is the latitude, and it is 
always of the same name with the greater of the two 
quantities. 

Examples. On the 10th of May, 1827, 1 observed 
the sun's meridian altitude to be 50°, and it was south 
of me at that time ; required the latitude of the place ? 

Answer. 57° 29' north. 

By calculation. 
90O C 
50 S., sun's altitude at noon. 



40 iV., the zenith's distance. 

17 29 N., the sun's declination 10th May 1827. 



57 29 N., the latitude sought 

2. On the 10th of May, 1827, the sun's meridian al- 
titude was observed to be 50°, and it was north of the 
observer at that time ; required the latitude of the 
place 1 

Answer. 22° 23' south. 

By calculation. 
990 0' 
50 N., sun's altitude at noon. 

40 S., the zenith's distance. 

17 29 AT., the sun's declination 10th May 1827. 



22 31 S., the latitude sought 

3. On the 5th of August, 1827, the sun's meridian 
altitude was observed to be 74° 30' north of the ob- 
server ; what was the latitude? 



THE TERRESTRIAL GLOBE. 105 

4. On the 19th of November, 1827, the sun's meri- 
dian altitude was observed to be 40° south of the ob- 
server ; what was the latitude ? 

5. At a certain place, where the clocks are two hours 
faster than at London, the sun's meridian altitude was 
observed to be 30 degrees to the south of the observer 
on the 21st of March ; required the place ? 

6. At the place where the clocks are 5 hours slower 
than at London, the sun's meridian altitude was ob- 
served to be 60° to the south of the observer on the 
16th of April, 1827 ; required the place ? 

Problem XLVIII. 

The length of the longest day at any place, not within 
the polar circles, being given, to find the latitude of 
that place. 

Rule. Bring the first point of Cancer or Capricorn 
to the brass meridian (according as the place is on the 
north or south side of the equator,) and set the index 
of the hour-circle to twelve : turn the globe westward 
on its axis till the index of the hour-circle has passed 
over as many hours as are equal to half the length of 
the day ; elevate or depress the pole till the sun's place 
(viz. Cancer or Capricorn) comes to the horizon ; then 
the elevation of the pole will show the latitude. 

Note. This problem will answer for any day in the year, as weU 
as the longest day, by bringing the sun's place to the brass meridian and 
proceeding as above. 

Or, Bring the middle of the analemma to the brass meridian, and 
set the index of the hour-circle to 12 ; turn the globe westward on its 
axis till the index has passed over as many hours as are equal to half 
the length of the day ; elevate or depress the pole till the day of the 



106 PROBLEMS PERFORMED WITH 

month coincides with the horizon, then the elevation of the pole will 
show the latitude. 

Examples. 1. In what degree of north latitude, 

and at what places is the length of the longest day 16^ 

hours ? 

Answer. In latitude 52°, and all places situated on, or near that pa- 
rallel of latitude, have the same length of the day. 

2. In what degree of south latitude, and at what 
places is the longest day 14 hours? 

3. In what degree of north latitude is the length of 
the longest day three times the length of the shortest 
night ? 

4. There is a town in Norway where the longest day 
is five times the length of the shortest night ; pray what 
is the name of the town ? 

5. In what latitude north does the sun set at seven 
o'clock on the 5th of April ? 

6. In what latitude south does the sun rise at five 
o'clock on the 25th of November ? 

7. In what latitude north is the 20th of May 16 
hours long ? 

8. In what latitude north is the night of the 15th of 
August 10 hours long? 

Problem XLIX. 

The latitude of a place and the day of the month being 
given , to find haio much the sun's declination must 
vary to make the day an hour longer or shorter than 
the given day. 

Rule. Find the sun's declination for the given 
day, and elevate the pole to that declination ; bring the 



THE TERRESTRIAL GLOBE. 107 

given place to the brass meridian, and set the index of 
the hour circle to twelve : turn the globe eastward on 
its axis till the given place comes to the horizon, and 
observe the hours passed over by the index. Then, if 
the days be increasing, continue the motion of the 
globe eastward till the index has passed over another 
half hour, and raise or depress the pole till the place 
comes again into the horizon, the elevation of the pole 
will show the sun's declination when the day is an hour 
longer than the given day ; but, if the days be decreas- 
ing, after the place is brought to the eastern part of 
the horizon, turn the globe westward till the index has 
passed over half an hour, then raise or depress the 
pole till the place comes a second time into the hori- 
zon, the last elevation of the pole will show the sun's 
declination when the day is an hour shorter than the 
given day. 

Or, 

Elevate the pole to the latitude of the place, find the 
sun's place in the ecliptic, bring it to the brass meri- 
dian, and set the index of the hour-circle to twelve ; 
turn the globe westward on its axis till the sun's place 
comes to the horizon, and observe the hours passed 
over by the index ; then, if the days be increasing, 
continue the motion of the globe westward till the in- 
dex has passed over another half hour, and observe 
what point of the ecliptic is cut by the horizon ; that 
point will show the sun's place when the day is an hour 
longer than the given day, whence the declination is 
readily found : but, if the days be decreasing, turn the 
globe eastward till the index has passed over half an 



108 PROBLEMS PERFORMED WITH 

hour, and observe what point of the ecliptic is cut by 
the horizon ; that point will show the sun's place when 
the day is an hour shorter than the given day. 

Or, by the analemma. 

Proceed exactly the same as above, only, instead of 
bringing the sun's place to the brass meridian, bring 
the analemma there, and instead of the sun's place, use 
the day of the month on the analemma. 

Examples. 1. How much must the sun's declina- 
tion vary that the day at London may be increased one 
hour from the 24th of February ? 

Answer. On the 24th of February the sun's declination is 9° 3& 
south, and the sun sets at a quarter past five ; when the sun sets at three 
quarters past five, his declination will be found to be about 4£° south, 
answering to the tenth of March : hence the declination has decreased 
5° 23', and the days have increased 1 hour in 14 days. 

2. How much must the sun's declination vary that 
the day at London may decrease one hour in length 
from the 26th of July ? 

Answer. The sun's declination on the 26th of July is 19° 38' north, 
and the sun sets at 49 min. past seven; when the sun sets at 19 min. 
past seven, his declination will be found to be 14° 43' north, answering 
to the 13th of August : hence the declination has decreased 5° 55', and 
the days have decreased one hour in 18 days. 

3. How much must the sun's declination vary from 
the 5th of April, that the day at Petersburg may in- 
crease one hour 7 

4. How much must the sun's declination vary from 
the 4th of October, that the day at Stockholm may de- 
crease one hour ? 

5. What is the difference in the sun's declination, 



THE TERRESTRIAL GLOBE. 109 

when he rises at seven o'clock at Petersburg, and when 
he sets at nine ? 

Problem L. 

To find the sun's right ascension, oblique ascension, ob- 
lique descension, ascensional difference, and time of 
rising and setting at any place. 

Rule. Find the sun's place in the ecliptic, and 
bring it to that part of the brass meridian which is 
numbered from the equator towards the poles ; the de- 
gree on the equator cut by the graduated edge of the 
brass meridian, reckoning from the point Aries east- 
ward, will be the sun's right ascension. 

Elevate the poles so many degrees above the horizon 
as are equal to the latitude of the place, bring the sun's 
place in the ecliptic to the eastern part of the horizon, 
and the degree on the equator cut by the horizon, 
reckoning from the point Aries eastward, will be the 
sun's oblique ascension. Bring the sun's place in the 
ecliptic to the western part of the horizon, and the de- 
gree on the equator cut by the horizon, reckoning from 
the point Aries eastward, will be the sun's oblique de- 
scension. 

Find the difference between the sun's right and ob- 
lique ascension ; or, which is the same thing, the dif- 
ference between the right ascension and oblique de- 
scension, and turn this difference into time by multi- 
plying by 4 : then, if the sun's declination and the 
latitude of the place be both of the same name, viz. 
both north or both south, the sun rises before six and 
sets after six, by a space of time equal to the ascen- 
k Y 



110 PROBLEMS PERFORMED WITH 

sional difference ; but if the sun's declination and the 
latitude be of contrary names, viz. the one north and 
the other south, the sun rises after six and sets before 
six. 

Examples. 1. Required the sun's right ascension, 
oblique ascension, oblique descension, ascensional dif- 
ference, and time of rising and setting at London, on 
the 15th of April ? 

Answer. The right ascension is 23° 30', the oblique ascension is 9° 
45', the ascensional difference (23° 30'— 9° 45'=) 13° 45', or 55 minutes 
of time ; consequently the sun rises 55 minutes before 6, or 5 min. past 
5, and sets 55 min. past 6. The oblique descension is 37° 15'; conse- 
quently the descensional difference is (37° 15'— 23° 30 / =) 13° 45', the 
same as the ascensional difference. 

2. What are the sun's right ascension, oblique ascen- 
sion, and oblique descension, on the 27th of October 
at London ; what is the ascensional difference, and at 
what time does the sun rise and set ? 

3. What are the sun's right ascension, declination, 
oblique ascension, rising amplitude, oblique descen- 
sion, and setting amplitude at London* on the 1st of 
May ; what is the ascensional difference, and at what 
time does the sun rfse and set ? 

4. What are the sun's right ascension, declination, 
oblique ascension, rising amplitude, oblique descen- 
sion, and setting amplitude, at Petersburg, on the 21st 
of June ; what is the ascensional difference, and what 
time does the sun rise and set ? 

5. What are the sun's right ascension, declination, 
oblique ascension, rising amplitude, oblique descen- 
sion, and setting amplitude, at Alexandria, on the 21st 



THE TERRESTRIAL GLOBE. Ill 

of December ; what is the ascensional difference, and 
what time does the sun rise and set ? 

Problem LI. 

Given the day of the month and the sun's amplitude 
at sunrise to find the latitude of the place of ob- 
servation. 

Rule. Find the sun's place in the ecliptic, and 
bring it to the eastern or western part of the horizon, 
(according as the eastern or western amplitude is 
given,) elevate or depress the pole till the sun's place 
coincides with the given amplitude on the horizon, 
then the elevation of the pole will show the latitude. 

Or, thus : 

Elevate the north pole to the complement* of the 
amplitude, and screw the quadrant of altitude upon the 
brass meridian over the same degree : bring the equi- 
noctial point Aries, to the brass meridian, and move 
the quadrant of altitude till the sun's declination for 
the given day (counted on the quadrant) coincides with 
the equator ; the number of degrees between the point 
Aries, and the graduated edge of the quadrant, will be 
the latitude sought. 

Examples. 1. The sun's amplitude at sunrise was 
observed to be 39° 48' from the east towards the north, 
on the 21st of June ; required the latitude of the place ? 

♦The complement of the amplitude is found by subtracting the ampli- 
plitude from 90°. This rule is exactly the same as above : for it is 
formed from a right-angled spherical triangle, the base being the com- 
plement of the amplitude, the perpendicular the latitude of the place, 
and the hypothenuse the complement of the sun's declination. 



112 PROBLEMS PERFORMED WITH 

Answer. 51° 32' north.* 

2. The sun's amplitude was observed to be 15° 30' 
from the east towards the north, at the same time his 
declination was 15° 30' ; required the latitude? 

3. On the 29th of May, when the sun's declination 
was 21° 30' north, his rising amplitude was known to 
be 22° northward of the east ; required the latitude ? 

4. When the sun's declination was 2° north, his ris- 
ing amplitude was 4° north of the east ; required the 
latitude ? 

Problem LII. 

Given two observed altitudes of the sun, the time elapsed 
between them, and the sun's declination, to find the 
latitude. 

Rule. Find the sun's declination, either by the globe 
or an ephemeris ; take the number of degrees contain- 
ed therein from the equator with a pair of compasses, 
and apply the same number of degrees upon the meri- 
dian passing through Libraf from the equator northward 
or southward, and mark where they extend to : turn 
the elapsed time into degrees, X and count those de- 
grees upon the equator from the meridian passing 
through Libra ; bring that point of the equator where 
the reckoning ends to the graduated edge of the brass 
meridian, and set off the sun's declination from that 

* See Keith's Trigonometry, fourth edition, page 285. 

t Any meridian will answer the purpose as well as that which passes 
through Libra ; on Adams' and on Cary's globes this merdlan is divided 
like the brass meridian. 

tSee the method of turning time into degrees. Prob. XIX. 



THE TERRESTRIAL GLOBE. 113 

point along the edge of the meridian, th? same way as 
before ; then take the complement of the first altitude 
from the equator in your compasses, and, with one foot 
in the sun's declination, and a fine pencil in the other 
foot, describe an arc; take the complement of the 
second altitude in a similar manner from the equator, 
and with one foot of the compasses fixed in the second 
point of the sun's declination, cross the former arc : 
the point of intersection brought to that part of the 
brass meridian which is numbered from the equator 
towards the poles, will stand under the degree of lati- 
tude sought 

Examples. 1. Suppose on the 4th of June. 1827, 
in north latitude, the sun's altitude at 29 minutes past 
10 in the forenoon, to be 65 c 24', and at 31 minutes 
past 12, 74 c 8' : required the latitude? 

Ansioer. The sun's declination i=? 22- 22' north, the elapsed time 
two hours two min. answering to 30- SO' ; the complement of the first 
altitude 24° 3&, the complement of the second altitude 15° 52', and the 
latitude sought 36° 57' north. 

2. Given the sun's declination 19° 39' north, his al- 
titude in the forenoon 38° 19', and, at the end of one 
hour and a half, the same morning, the altitude was 
50° 25' ; required the latitude of the place, supposing 
it to be north ? 

3. When the sun's declination was 22° 40' north, 
his altitude at 10 h. 54 m. in the forenoon was 53° 29-', 
and at 1 h. 17 m. in the afternoon it was 52° 48' ; re- 
quired the latitude of the place of observation, sup- 
posing it to be north? 

4. In north latitude, when the sun's declination was 
22° 23' south, the sun's altitude in the afternoon was 

k 2 Y 2 



114 PROBLEMS PERFORMED WITH 

observed to be 14° 46', and after 1 h. 22 m. had elapsed, 
his altitude was 8° 27'; required the latitude? 

Problem LIIL 

The day and hour being given when a solar eclipse 
will happen, to find where it will be visible. 

Rule. Find the sun's declination, and elevate the 
pole agreeably to that declination ; bring the place at 
which the hour is given to that part of the brass meri- 
dian which is numbered from the equator towards the 
poles, and set the index of the hour-circle to twelve ; 
then, if the given time be before noon, turn the globe 
westward till the index has passed over as many hours 
as the given time wants of noon ; if the time be past 
noon, turn the globe eastward as many hours as it is 
past noon, and exactly under the degree of the sun's 
declination on the brass meridian you will find the 
place on the globe where the sun will be vertically 
eclipsed :* at all places within 70 degrees of this place, 
the eclipse may f be visible, especially if it be a total 
eclipse. 

Example. On the 11th of February, 1804, at 27 
min. past ten o'clock in the morning at London, there 
was an eclipse of the sun, where was it visible, sup- 

* The effect of parallax is so great, that an eclipse may not be visi- 
ble even where the sun is vertical. 

t When the moon is exactly in the node, and when the axis of the 
moon's shadow and penumbra pass through the centre of the earth, the 
breadth of the earth's surface under the penumbral shadow is 70° 20'; 
but the breadth of this shadow is variable; and if it be not accurately 
determined by calculation, it is impossible to tell by the globe to what 
extent an eclipse of the sun will be visible. 



THE TERRESTRIAL GLOBE. 115 

posing the moon's penumbral shadow to extend north- 
ward 70 degrees from the place where the sun was 
vertically eclipsed ? 
Answer. London, &c. 

Problem LIV. 

The day and hour being given when a lunar eclipse will 
happen, to find where it will be visible. 

Rule. Find the sun's declination for the given day, 
and note whether it be north or south ; if it be north, ele- 
vate the south pole so many degrees above the horizon 
as are equal to the declination ; if it be south, elevate 
the north pole in a similar manner ; bring the place at 
which the hour is given to that part of the brass meri- 
dian which is numbered from the equator towards the 
poles, and set the index of the hour-circle to twelve ; 
then, if the given time be before noon, turn the globe 
westward as many hours as it wants of noon ; if after 
noon, turn the globe eastward as many hours as it is 
past noon ; the place exactly under the degree of the 
sun's declination will be the antipodes of the place 
where the moon is vertically eclipsed, set the index 
of the hour-circle again to twelve, and turn the globe on 
its axis till the index has passed over twelve hours ; 
then to all places above the horizon the eclipse will be 
visible ; to those places along the western edge of the 
horizon, the moon will rise eclipsed ; to those along 
the eastern edge she will set eclipsed ; and to that place 
immediately under the degree of the sun's declination, 
reckoning towards the elevated pole, the moon will be 
vertically eclipsed. 



116 PROBLEMS PERFORMED WITH 

Example. On the 26th of January, 1804, at 58 min. 
past seven in the afternoon at London, there was an 
eclipse of the moon ; where was it visible ? 

Answer. It was visible to the whole of Europe, Africa, and the 
continent of Asia. 

Problem LV. 

To find the time of the year tohen the Sun or Moon will 
be liable to be eclipsed. 

Rule 1. Find the place of the moon's nodes, the 
time of new moon, and the sun's longitude at that time, 
by an ephemeris ; then if the sun be within 17 de- 
grees of the moon's node, there will be an eclipse of 
the sun. 

2. Find the place of the moon's nodes, the time of 
full moon, and the sun's longitude at that time, by an 
ephemeris: then, if the sun's longitude be within 12 
degrees of the moon's node, there will be an eclipse of 
the moon. 

Or, without the ephemeris. 

The mean annual variation of the moon's nodes is 
19° 19' 44" and the place of the node for the first of 
January 1827 being 2° 2' in =£=, its place for any other 
time may therefore be found. 

ExAMPLEs.l.Onthe9thof June, 1827, there will be 
a full moon, at which time the place of the moon's 
node is 7° in =^ and the sun's longitude tf, 17° 48'; will 
an eelipse of the moon happen at that time ? 

Answer, Here the sun's longitude is not within 12 degrees of the 



THE TERRESTRIAL GLOBE. 117 

moon's node, therefore there will be no eclipse of the moon. — When 
the sun is in one of the moon's nodes at the time of full moon, the moon 
is in the other node, and the earth is directly between them. 

2. There will be a new moon on the 7th of June, 
1827, at which time the place of the moon's node will 
be =&, 12° 43' and the sun's longitude « 15° 54'; will 
there be an eclipse of the sun at that time? 

3. There will be a new moon on the 18th of De- 
cember 1827, at which time the place of the moon's 
node will be =~= 2° 24' and the sun's longitude ty 25° 
51' ; will there be an eclipse of the sun at that time ? 

4. On the 3d of November, 1827, there will be a 
full moon, at which time the place of the moon's node 
will be -= 4° 56', and the sun's longitude =£= 10° 18' ; 
will there be an eclipse of the moon at that time? 

5. On the 25th of April, 1827, there will be a new 
moon, at which time the place of the moon's node is =~= 
15° 19' and the sun's longitude <Y> 4° 29' ; will there be 
an eclipse of the sun at that time ? 

6. On the 20th of October, 1827, there will be a 
new moon, at which time the place of the moon's node 
is -=5° 38' and the sun's longitude ty 26° 19'; will 
there be an eclipse of the sun at that time ? 

Problem LVI. 

To explain the phenomenon of the harvest moon. 

Definition 1. The harvest moon, in north latitude, 
is the full moon which happens at, or near the time of 
the autumnal equinox ; for, to the inhabitants of north 
latitude, whenever the moon is in Pisces or Aries (and 
she is in these signs twelve times in a year,) there is 



118 PROBLEMS PERFORMED WITH 

very little difference between her times of rising for 
several nights together, because her orbit is at these 
times nearly parallel to the horizon. This peculiar 
rising of the moon passes unobserved at all other times 
of the year except in September and October ; for there 
never can be a full moon except the sun be directly 
opposite to the moon ; and as this particular rising of 
the moon can only happen when the moon is in X Pisces 
or cp Aries, the sun must necessarily be either in tij 
Virgo or =^ Libra at that time, and these signs answer 
to the months of September and October. 

Definition 2. The harvest moon, in south latitude, 
is the full moon which happens at, or near, the time of 
the vernal equinox ; for, to the inhabitants of south la- 
titude, whenever the moon is in tt^ Virgo or =^ Libra 
her orbit is nearly parallel to the horizon : but when 
the full moon happens in ty Virgo or =^= Libra, the sun 
must be either in X Pisces or °P Aries. Hence it ap- 
pears that the harvest moons are just as regular in south 
latitude as they are in north latitude, only they happen 
at contrary times of the year. 

Rule for performing the problem. — 1. For north 
latitude. Elevate the north pole to the latitude of the 
place, put a patch or make a mark in the ecliptic on 
the point Aries, and upon every twelve degrees pre- 
ceding and following that point, till there be ten or ele- 
ven marks ; bring that mark which is the nearest to 
Pisces to the eastern edge of the horizon, and set the 
index to 12 ; turn the globe westward till the other 
marks successive! v come to the horizon, and observe 



THE TERRESTRIAL GLOBE. 219 

the hours passed over by the index ; the intervals of 
time between the marks coming to the horizon will 
show the diurnal difference of time between the moon's 
rising. If these marks be brought to the western edge 
of the horizon in the same manner, you will see the 
diurnal difference of time between the moon's setting: 
for, when there is the smallest difference between the 
times of the moon's rising, there will be the greatest 
difference between the times of her setting ; and, on 
the contrary, when there is the greatest difference be- 
tween the times of the moon's rising, there will be the 
least difference between the times of her setting. 

JNote. As the moon's nodes vary their position and form a complete 
revolution in about nineteen years, there will be a regular period of 
all the varieties which can happen in the rising and setting of the moon 
during that time. The following table (extracted from Ferguson's As- 
tronomy,) shows in what j^ears the harvest moons are the least and most 
beneficial, with regard to the times of their rising, from 1823 to 1860. 
The columns of years under the letter L are those in which the har- 
vest moons are least beneficial, because they fall about the descending 
node ; and those under M are the most beneficial, because they fall 
about the ascending node. 



L L L L 

1826 1831 1845 1849 

1827 1832 1846 1850 

1828 1833 1847 1851 

1829 1834 1848 1852 

1830 1844 



M M M M 

1823 1837' 1842 1856 

1824 1838 1843 1857 

1825 1839 1853 1858 

1835 1840 1854 1859 

1836 1841 1855 1860 



2. For smith latitude. Elevate the south pole to the 
latitude of the place, put a patch or make a mark 
on the ecliptic on the point Libra, and upon every 
twelve degrees preceding and following that point, till 
there be ten or eleven marks; bring that mark which 
is the nearest to Virgo, to the eastern edge of the hori- 
zon, and set the index to 12 ; turn the globe westward 



120 PROBLEMS PERFORMED WITH 

till the other marks successively come to the horizon, 
and observe the hours passed over by the index ; the 
intervals of time between the marks coming to the ho- 
rizon will be the diurnal difference of time between 
the moon's rising, &c. as in the foregoing part of the 
problem.* 

Problem LVII. 

The day and hour of an eclipse of any one of the satel- 
lites of Jupiter being given, to find upon the globe all 
those places where it will be visible* 

Rule. Find the sun's declination for the given day, 
and elevate the pole to that declination; bring the 
place at which the hour is given to the brass meridian, 
and set the index of the hour-circle to 12 ; then, if the 
given time be before noon, turn the globe westward as 
many hours as it wants of noon ; if after noon, turn the 
globe eastward as many hours as it is past noon ; fix 
the globe in this position : Then, 

1. If Jupiter rise after the sun y "\ that is, if he be an 
evening star, draw a line along the eastern edge of the 
horizon with a black lead pencil, this line will pass over 
all places on the earth where the sun is setting at the 



* This solution is on a supposition that the moon keeps constantly in 
the ecliptic, which is sufficiently accurate for illustrating the problem. 
Otherwise the latitude and longitude of the moon, or her right ascension 
and declination, may be taken from the ephemeris, at the time of full 
moon, and a few days preceding and following it ; her place will then 
be truly marked on the globe. 

t Jupiter rises after the sun, when his longitude is greater than the 
sun's longitude. 



THE TERRESTRIAL GLOBE. 121 

given hour ; turn the globe westward on its axis till 
as many degrees of the equator have passed under the 
brass meridian as are equal to the difference between 
the sun's and Jupiter's right ascension ; keep the globe 
from revolving on its axis, and elevate the pole as many 
degrees above the horizon as are equal to Jupiter's de- 
clination, then draw another line with a pencil along 
the eastern edge of the horizon : the eclipse will be 
visible to every place between these lines, viz. from 
the time of the sun's setting to the time of Jupiter's 
setting. 

2. If Jupiter rise before the sun, # that is, if he be 
a morning star, draw a line along the western edge of 
the horizon with a black lead pencil, this line will pass 
over all places of the earth where the sun is rising at 
the given hour ; turn the globe eastward on its axis 
till as many degrees of the equator have passed under 
the brass meridian as are equal to the difference be- 
tween the sun's and Jupiter's right ascension ; keep 
the globe from revolving on its axis, and elevate the 
pole as many degrees above the horizon as are equal 
to Jupiter's declination, then draw another line with a 
pencil along the western edge of the horizon ; the 
eclipse will be visible to every place between these 
lines, viz. from the time of Jupiter's rising to the time 
of the sun's rising. 

Examples. 1. On the 13th of January, 1805, there 
was an immersion of the first satellite of Jupiter at 



* Jupiter rises before the sun when his longitude is less than the sun's 
longitude. 

I z 



122 FK0BLE3IS PERFORMED WITH 

9 m. 3 sec. past five o'clock in the morning at Green- 
wich ; where was it visible ? 

Answer. In this example the longitude of the sun exceeds the lon- 
gitude of Jupiter, therefore Jupiter was a morning star, his declination 
being 19° 16' S. and his longitude 7 signs 29° 46', by the Nautical Al- 
manac : his right ascension and the sun's right ascension may be found 
by the globe ; for, if Jupiter's longitude in the ecliptic be brought to the 
brass meridian, his place will stand under the degree of his declina- 
tion;* and his right ascension will be found on the equator, reckoning 
from Aries. This eclipse was visible at Greenwich, the greater part 
of Europe, the west of Africa, Cape Verd islands, &c. 

2. On the 5th of January, 1827, at 44 min. 2 sec. 
past seven o'clock in the morning, at Greenwich, there 
will be an immersion of the first satellite of Jupiter; 
where will the eclipse be visible ? Jupiter's longitude 
at that time being 6 signs 13° 41' and his declination 
4° 10' south. 

3. On the 5th of June, 1827, at 14 min. 8 sec. past 
eight o'clock in the evening, at Greenwich, there will 
be an emersion of the first satellite of Jupiter ; where 
will the eclipse be visible? Jupiter's longitude at 
that time being 6 signs 4° 31' and his declination 0° 
30' south. 

4. On the 2d of December, 1827, at 39 min. 4 sec. 
past six o'clock in the morning, at Greenwich, there 
will be an immersion of the first satellite of Jupiter; 
where will the eclipse be visible ? Jupiter's longitude 

* This is on supposition that Jupiter moves in the ecliptic, and, as he 
deviates but little therefrom, the solution by this method will be suf- 
ficiently accurate. To know if an eclipse of any one of the satellites 
of Jupiter will be visible at any places we are directed by the Nauti- 
cal Almanac to " find whether Jupiter be 8° above the horizon of the 
place, and the sun as much below it." 



THE TERRESTRIAL GLOBE. 123 

at that time being 7 signs 3° 59' and his declination 
1° 5' north. 

Problem LVIII. 

To place the terrestrial globe in the sun-shine, so that 
it may represent the natural position of the earth. 

Rule. If you have a meridian line* drawn upon a 
horizontal plane, set the north and south points of the 
wooden horizon of the globe directly over this line ; 
or, place the globe directly north and south by the ma- 
riner's compass, taking care to allow for the variation ; 
bring the place in which you are situated to the brass 
meridian, and elevate the pole to its latitude ; then the 
globe will correspond in every respect with the situa- 
tion of the earth itself. The poles, meridians, parallel 
circles, tropics, and all the circles on the globe, will 
correspond with the same imaginary circles in the 
heavens ; and each point, kingdom, and state, will be 
turned towards the real one, which it represents. 

While the sun shines on the globe, one hemisphere 
will be enlightened, and the other will be in the shade : 
thus, at one view, may be seen all places on the earth 
which have day, and those which have night.f 

If a needle be placed perpendicularly in the middle 
of the enlightened hemisphere, (which must of course 

* As a meridian line is useful for fixing a horizontal dial, and for 
placing a globe directly north and south, &c. the different methods of 
drawing a line of this kind will precede the problems on dialling. 

tFor this part of ^he problem it would be more convenient if the 
globe could be properly supported without the frame of it, because the 
shadow of its stand, and that of its horizon, will darken several parts of 
the surface of the globe, which would otherwise be enlightened. 



124 PROBLEMS PERFORMED WITH 

be upon the parallel of the sun's declination for the 
given day,) it will cast no shadow, which shows that 
the sun is vertical at that point ; and if a line be drawn 
through this point from pole to pole, it will be the me- 
ridian of the place where the sun is vertical, and every 
place upon this line will have noon at that time ; all 
places to the west of this line will have morning, and 
all places to the east of it afternoon. Those inhabitants 
who are situated on the circle which is the boundary 
between light and shade, to the westward of the meri- 
dian where the sun is vertical, will see the sun rising ; 
those in the same circle to the eastward of this meri- 
dian will see the sun setting. Those inhabitants to- 
wards the north of the circle, which is the boundary 
between light and shade, will perceive the sun to the 
southward of them, in the horizon ; and those who are 
in the same circle towards the south, will see the sun 
in a similar manner to the north of them. 

If the sun shine beyond the north pole at the given 
time, his declination is as many degrees north as he 
shines over the pole ; and all places at that distance 
from the pole will have constant day, till the sun's de- 
clination decreases, and those at the same distance 
from the south pole will have constant night. 

If the sun do not shine so far as the north pole at 
the given time, his declination is as many degrees south 
as the enlightened part is distant from the pole ; and 
all places within the shade, near the pole, will have 
constant night, till the sun's declination increases 
northward. While the globe remains steady in the po- 
sition it was first placed when the sun is westward of 



THE TERRESTRIAL GLOBE. 125 

the meridian, you may perceive on the east side of it, 
in what manner the sun gradually departs from place 
to place as the night approaches ; and when the sun is 
eastward of the meridian, you may perceive on the 
western side of it, in what manner the sun advances 
from place to place as the day approaches. 

Problem LIX. 
The latitude of a place being given, to find the hour of 
the day at any time when the sun shines. 
Rule 1. Place the north and south points of 
the horizon of the globe directly north and south 
upon a horizontal plane, by a meridian line, or by a 
mariner's compass, allowing for the variation, and ele- 
vate the pole to the latitude of the place; then, if the 
place be in north latitude, and the sun's declination be 
north, the sun will shine over the north pole ; and if a 
long pin be fixed perpendicularly in the direction of the 
axis of the earth, and in the centre of the hour-circle, 
its shadow will fall upon the hour of the day, the figure 
XII of the hour-circle being first set to the brass meri- 
dian. If the place be in north latitude, and the sun's 
declination be above ten degrees south, the sun will 
not shine upon the hour-circle at the north pole. 

Rule 2. Place the globe due north and south upon 
a horizontal plane, as before, and elevate the pole to 
the latitude of the place ; find the sun's place in the 
ecliptic, bring it to the brass meridian, and set the in- 
dex of the hour-circle to XII ; stick a needle perpen- 
dicularly in the sun's place in the ecliptic, and turn 
the globe on its axis till the needle casts no shadow ; 
fix the globe in this position, and the index will show 
12 z2 



126 PROBLEMS PERFORMED WITH 

the hour before 12 in the morning, or after 12 in the 
afternoon. 

. Rule 3. Divide the equator into 24 equal parts 
from the point Aries, on which place the number VI ; 
and proceed westward VII, VIII, IX, X, XI, XII, I, II, 
III, IV, V, VI, which will fall upon the point Libra, 
VII, VIII, IX, X, XI, XII, I, II, III, IV, V;* elevate 
the pole to the latitude, place the globe due north and 
south upon a horizontal plane, by a meridian line, or 
a good mariner's compass, allowing for the variation, 
and bring the point Aries to the brass meridian ; then 
observe the circle which is the boundary between light 
and darkness westward of the brass meridian ; and it 
will intersect the equator in the given hour in the morn- 
ing ; but, if the same circle be eastward of the bTass 
meridian, it will intersect the equator in the given hour 
in the afternoon. 

Or, Having placed the globe upon a true horizontal 
plane, set it due north and south by a meridian line ; 
elevate the pole to the latitude, and bring the point 
Aries to the brass meridian, as before ; then tie a small 
string, with a noose, round the elevated pole, stretch 
its other end beyond the globe, and move it so that the 
shadow of the string may fall upon the depressed axis ; 
at that instant its shadow upon the equator will give 
the hour.f 

* On Adams' globes the antarctic circle is thus divided, by which 
the problem may be solved. 

t The learner must remember that the time shown in this problem 
is solar time, as shown by a sun-dial ; and, therefore, to agree with a 
good clock or watch, it must be corrected by a table of equation of time. 
See a table of this kind among the succeeding problems. 



THE TERRESTRIAL GLOBE. 127 

Problem LX. 

To find the sun's altitude, by placing the globe in the 
sun-shine. 

Rule. Place the globe upon a truly horizontal 
plane, stick a needle perpendicularly over the north 
pole,* in the direction of the axis of the globe, and 
turn the pole towards the sun, so that the shadow of 
the needle may fall upon the middle of the brass meri- 
dian ; then elevate or depress the pole till the needle 
casts no shadow ; for then it will point directly to the 
sun ; the elevation of the pole above the horizon will be 
the sun's altitude. 

Problem LXI. 

To find the surfs declination, Ms place iy, the ecliptic, 
and his azimuth, by placing the globe in the sun- 
shine. 

Rule. Place the globe upon a truly horizontal 
plane, in a north and south direction by a meridian 
line, and elevate the pole to the latitude of the place ; 
then, if the sun shine beyond the north pole, his decli- 
nation is as many degrees north as he shines over the 
pole ; if the sun do not shine so far as the north pole, 
his declination is as many degrees south as the enlight- 
ened part is distant from the pole. The sun's declina- 
tion being found, his place may be determined by 
Problem XX. 

* It would be an improvement on the globes were our instrument- 
makers to drill a very small hole in the brass meridian over the north 
pole. 



128 PROBLEMS PERFORMED WITH 

Stick a needle in the parallel of the sun's declina- 
tion for the given day,* and turn the globe on its axis 
till the needle casts no shadow : fix the globe in this 
position, and screw the quadrant of altitude over the 
latitude ; bring the graduated edge of the quadrant to 
coincide with the sun's place, or the point where the 
needle is fixed, and the degree on the horizon will 
show the azimuth. 



CHAPTER III. 

PROBLEMS PERFORMED WITH THE CELESTIAL GLOBE. 

Problem LXII. 

To find the right ascension and declination of the sun, 
• or a star. 

Rule. Bring the sun or star to that part of the brass 
meridian which is numbered from the equinoctial to- 
wards the poles ; the degree on the brass meridian is 
the declination, and the number of degrees on the 
equinoctial, between the brass meridian and the point 
Aries, is the right ascension. 

Or, Place both the poles of the globe in the horizon, 
bring the sun or star to the eastern part of the horizon ; 
then the number of degrees which the sun or star is 
northward or southward of the east, will be the decli- 
nation north or south ; and the degrees on the equinoc- 

* On Adams' globes the torrid zone is divided into degrees by dotted 
lines, so that the parallel of the sun's declination is instantly found : in 
using other globes, observe the declination on the brass meridian, and 
stick a needle perpendicularly in the globe under that degree. 



THE CELESTIAL GLOBE. 129 

tial, from Aries to the horizon, will be the right ascen- 
sion. 

Examples. 1. Required the right ascension and 
declination of * Dubhe, in the back of the Great Bear. 

Answer. Right ascension 162° 49', declination 62° 4& N. 

2. Required the right ascensions and declinations 
of the following stars ? 



y, Algenib, in Pegasus. 
«, Scheder, in Cassiopeia. 
fi 9 Mirachy in Andromeda. 
*, Acherner, in Eridanus. 
«, Menkar, in Cetus. 
£, Algol, in Perseus. 
*, Aldebarariy in Taurus. 
», Capella, in Auriga. 
im Rigel, in Orion. 



r> Bellatrix, in Orion. 
*, Betelgeux, in Orion. 
*, Canopus, in Argo Na- 

vis. 
*, Procyon, in the Little 

Dog. 
r, Algorab, in the Crow. 
*, Arcturus, in Bootes. 
«, Vendemiatrixy in Virgo. 



Problem LXIII. 

To find the latitude and longitude of a star.* 
Rule. Place the upper end of the quadrant of alti- 
tude on the north or south pole of the ecliptic, ac- 
cording as the star is on the north or south side of the 
ecliptic, and move the other end till the star comes to 
the graduated edge of the quadrant : the number of de- 
grees between the ecliptic and the star is the latitude ; 
and the number of degrees on the ecliptic, reckoned 
eastward from the point Aries to the quadrant, is the 
longitude. 

Or, Elevate the north or south pole 66 J° above the 
horizon, according as the given star is on the north or 

* The latitudes and longitudes of the planets must be found from an 
ephemeris. 



130 PROBLEMS PERFORMED WITH 

south side of the ecliptic ; bring the pole of the eclip- 
tic to that part of the brass meridian which is number- 
ed from the equinoctial towards the pole : then the 
ecliptic will coincide with the horizon ; screw the 
quadrant of altitude upon the brass meridian over the 
pole of the ecliptic ; keep the globe from revolving on 
its axis, and move the quadrant till its graduated edge 
comes over the given star : the degree on the quadrant 
cut by the star is its latitude ; and the sign and degree 
on the ecliptic cut by the quadrant show its longitude. 
Examples. 1. Required the latitude and longitude 
of * Aldebaran in Taurus ? 

Answer. Latitude 5° 28' S. longitude 2 signs 6° 53'; or 6° 53' in 
Gemini. 

2. Required the latitudes and longitudes of the fol- 
lowing stars 1 



«, Markab, in Pegasus. 
fi y Scheat, in Pegasus. 
«., Fomalhaut, in the S. 

Fish. 
*, Deneb, in Cygnus. 
*, Altair, in the Eagle. 
fi, Albireo, in Cygnus. 



«, Vega, in Lyra. 
r, Rastaben, in Draco. 
*, Antares, in the Scor- 
pion. 
*, Arcturus, in Bootes. 
£, Pollux, in Gemini. 
£, Rigel, in Orion. 



Problem LXIV. 

The right ascension and declination of a star, the moon, 
a planet, or of a comet, being given, to find its place 

on the globe. 

Rule. Bring the given degrees of right ascension 
to that part of the brass meridian which is numbered 
from the equinoctial towards the poles : then under 



THE CELESTIAL GLOBE. 131 

the given declination on the brass meridian you will 
find the star, or place of the planet. 

Examples. 1. What star has 261° 29' of right as- 
cension, and 52° 27' north declination? 

Answer. £ in Draco. 

2. On the 31st of January, 1825, the moon's right 
ascension was 91° 21', and her declination 23° 19'; 
find her place on the globe at that time. 

Answer. In the milky way, a little above the left foot of Castor. 

3. What stars have the following right ascensions 
md declinations ? 

Right Ascensions. Declinations. 



7 c 


19' 


55 


11 


11 


59 


25 


54 


19 


46 


32 


9 


53 


54 


23 


76 


14 


8 



nati< 
26' 


)ns. 

N. 


38 


N. 


50 


N. 


34 


S. 


29 


N. 


27 


S. 



Right Ascensions. 


Declinations. 


83° 6' 


34° 11' S. 


86 13 


44 55 N. 


99 5 


16 26 S. 


110 27 


32 19 N. 


113 16 


28 30 N. 


129 2 


7 8 N. 



4. On the 1st of December, 1827, the moon's right 
ascension at midnight will be 50° 58', and her de- 
clination 16° 58' N.; find her place on the globe. 

5. On the 1st of May, 1827, the declination of Ve- 
nus will be 1° 11' S. and her right ascension 0° 4'; 
find her place on the globe at that time. 

6. On the 19th of January, 1827, the declination of 
Jupiter will be 4° 21' S. and his right ascension 12° 
55'; find his place on the globe at that time. 



132 



PROBLEMS PERFORMED WITH 



Problem LXV. 

The latitude and longitude of the moon, a star or a 
planet, given, to find its place on the globe* 

Rule. Place the division of the quadrant of altitude 
marked 0, on the given longitude in the ecliptic, and 
the upper end on the pole of the ecliptic ; then, under 
the given latitude, on the graduated edge of the qua- 
drant, you will find the star, or place of the moon or 
planet. 

Examples. 1. What star has signs 6° 16' of lon- 
gitude, and 12° 36' N. latitude? 

Answer, y in Pegasus. 

2. On the 5th of June, 1827, at midnight, the moon's 
longitude will be 6 9 23° 41'; and her latitude 1° 49' 
S.; find her place on the globe. 

3. What stars have the following latitudes and longi- 
tudes ? 



Latitudes. 


Longitudes. 


Latitudes. 


Longitudes. 


12° 35' S. 


r n° 25' 


39° 33' S. 


3 s 11° 13' 


5 29 S. 


2 6 53 


10 4 N. 


3 17 21 


31 8 S. 


2 13 56 


27 N. 


4 26 57 


22 52 N. 


2 18 57 


44 20 N. 


7 9 22 


16 3 S. 


2 25 51 


21 6 S, 


11 56 



4. On the first of June, 1827, the longitudes and 
latitudes of the planets will be as follow : required their 
places on the globe 1 



Longitudes, 


Latitudes. 


Longitudes. 


Latitudes. 


$ 2 8 0° 54' 


0° 29' S. 


4 6 8 4° 28' 


1°27'N. 


? 1 7 1 


1 52 S. 


b 3 5 47 


32 S. 


2 2 22 12 


46 N. 


V 9 27 52 


21 5S. 



THE CELESTIAL GLOBE. 133 

Problem LXVI. 

The day and hour, and the latitude of a place being 
given, to find, what stars are rising, setting, culmina- 
ting, fyc. 

Rule. Elevate the pole to the latitude of the place, 
find the sun's place in the ecliptic, bring it to the brass 
meridian, and set the index of the hour-circle to 12 ; 
then, if the time be before noon, turn the globe east- 
ward on its axis till the index has passed over as many 
hours as the time wants of noon ; but, if the time be 
past noon, turn the globe westward till the index has 
passed over as many hours as the time is past noon : 
then all the stars on the eastern semi-circle of the ho- 
rizon will be rising, those on the western semi-circle 
will be setting, those under the brass meridian above 
the horizon will be culminating, those above the hori- 
zon will be visible at the given time and place, those 
below will be invisible. 

If the globe be turned on its axis from east to west, 
those stars which do not go below the horizon never 
set at the given place ; and those which do not come 
above the horizon never rise ; or, if the given latitude 
be subtracted from 90 degrees, and circles be described 
on the globe, parallel to the equinoctial, at a distance 
from it equal to the degrees in the remainder, they 
will be the circles of perpetual apparition and occulta- 
tion. 

Examples. 1. On the 9th of February, when it is 
nine o'clock in the evening at London, what stars are 
m 2 A 



134 PROBLEMS PERFORMED WITH 

rising, what stars are setting, and what stars are on the 

meridian ? 

Answer. Alphacca, in the northern Crown is rising ; Arcturus and 
Mirach, in Bootes, just above the horizon ; Sirius on the meridian ; 
Procyon and Castor and Pollux a little east of the meridian. The con- 
stellations Orion, Taurus, and Auriga, a little west of the meridian : 
Markab, in Pegasus, just below the western edge of the horizon, &c. 

2. On the 20th of January, at two o'clock in the morn- 
ing at London, what stars are rising, what stars are 
setting, and what stars are on the meridian ? 

Answer. Vega in Lyra, the head of the Serpent, Spica Virginis, &c. 
arc rising ; the head of the Great Bear, the claws of Cancer, &c. on the 
meridian ; the head of Andromeda, the neck of Cetus, and the body of 
Columba Noachi, &c. are setting. 

3. At ten o'clock in the evening at Edinburgh, on 
the 15th of November, what stars are rising, what stars 
are setting, and what stars are on the meridian ? 

4. What stars do not set in the latitude of London, 
and at what distance from the equinoctial is the circle 
of perpetual apparition ? 

5. What stars do not rise to the inhabitants of Edin- 
burgh, and at what distance from the equinoctial is the 
circle of perpetual occultation ? 

6. What stars never rise at Otaheite, and what stars 
never set at Jamaica? 

7. How far must a person travel southward from 
London to lose sight of the Great Bear ? 

8. What stars are continually above the horizon at 
the north pole, and what stars are constantly below the 
horizon thereof? 



THE CELESTA! GLOBE. 135 

Problem LXVII. 

The latitude of a place, day of the month, and hour 
being given, to place the globe in such a manner as 
to represent, the heavens at that time ; in order to find 
out the relative situations and names of the constella- 
tions and remarkable stars. 

Rule. Take the globe out into the open air, on 
a clear star-light night, where the surrounding horizon 
is uninterrupted by different objects ; elevate the pole 
to the latitude of the place, and set the globe due north 
and south by a meridian line, or by a mariner's com- 
pass, taking care to make a proper allowance for the 
variation ; find the sun's place in the ecliptic, bring it 
to the brass meridian and set the index of the hour- 
circle to 12 ; then, if the time be after noon, turn the 
globe westward on its axis, till the index has passed 
over as many hours as the time is past noon ; but, if 
the time be before noon, turn the globe eastward till 
the index has passed over as many hours as the time 
wants of noon ; fix the globe in this position, then the 
flat end of a pencil being placed on any star on the 
globe so as to point towards the centre, the other end 
will point to that particular star in the heavens. 

Problem LXVIII. 

To find when any star, or planet, will rise, come to the 
meridian, and set at any given place. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place ; find 



136 PROBLEMS PERFORMED WITH 

the sun's place in the ecliptic, bring it to the brass 
meridian, and set the index of the hour-circle to 12. 
Then if the star or planet be below the horizon, turn 
the globe westward till the star or planet comes to the 
eastern part of the horizon, the hours passed over by 
the index will show the time from noon when it rises ; 
and, by continuing the motion of the globe westward 
till the star, &c. comes to the meridian, and to the west- 
ern part of the horizon successively, the hours passed 
over by the index will show the time of culminating 
and setting. 

If the star, &c. be above the horizon and east of the 
meridian, find the time of culminating, setting, and 
rising, in a similar manner. If the star, &c. be above 
the horizon west of the meridian, find the time of set- 
ting, rising, and culminating, by turning the globe 
westward on its axis. 

Examples. 1. At what time will Arcturus rise, 
come to the meridian, and set, at London, on the 7th 
of September ? 

Answer. It will rise at seven o'clock in the morning, come to the 
meridian at three in the afternoon, and set at eleven o'clock at night. 

2. On the 1st of August, 1805, the longitude of Ju- 
piter was 7 signs 26 deg. 34 min., and his latitude 45 
min. N. ; at what time did he rise, culminate, and set, 
at Greenwich, and whether was he a morning or an 
evening star 1 

Answer. Jupiter rose at half past two in the afternoon, came to the 
meridian at about ten minutes to seven, and set at a quarter past eleven 
in the evening. Here Jupiter was an evening star, because he set after 
the sun. 



THE CELESTIAL GLOBE. 137 

3. At what time does Siriiis rise, set, and come to 
the meridian of London, on the 31st of January ? 

4. On the 1st of January, 1827, the longitude of 
Venus will be 8 signs 27 deg. 10 min. and her latitude 
1 deg. 29 min. N.; at what time will she rise, culminate, 
and set at Paris, and whether will she be a morning or 
an evening star ? 

5. At what time does Aldebaran rise, come to the 
meridian, and set at Dublin, on the 25th of November? 

6. On the first of February, 1827, the longitude of 
Mars will be 11 signs 26 deg. 26 min., and latitude 
deg. 32 min. S. ; at what time will he rise, set, and 
come to the meridian of Greenwich ? 

Problem LX1X. 

To find the amplitude of any star, its oblique ascension 
and descension, and its diurnal arc for any given day. 

Rule. Elevate the pole to the latitude of the place, 
and bring the given star to the eastern part of the ho- 
rizon ; then the number of degrees between the star 
and the eastern point of the horizon will be its rising 
amplitude ; and the degree of the equinoctial cut by 
the horizon will be the oblique ascension : set the index 
of the hour-circle to 12, and turn the globe westward 
till the given star comes to the western edge of the ho- 
rizon ; the hours passed over by the index will be the 
star's diurnal arc, or continuance above the horizon. 
The setting amplitude will be the number of degrees 
between the star and the western point of the horizon, 
and the oblique descension will be represented by that 
w2 2 a 2 



138 PROBLEMS PERFORMED WITH 

degree of the equinoctial which is intersected by the 
horizon, reckoning from the point Aries. 

Examples. 1. Required the rising and setting am- 
plitude of Sirius, its oblique ascension, oblique descen- 
sion, and diurnal arc, at London ? 

Answer. The rising amplitude is 27 deg. to the south of the east ; 
setting amplitude 27 deg. south of the west ; oblique ascension 120 deg.; 
oblique descension 77 deg.; and diurnal arc 9 hours 6 minutes. 

2. Required the rising and setting amplitude of Al- 
debaran, its oblique ascension, oblique descension, and 
diurnal arc, at London ? 

3. Required the rising and setting amplitude of 
Arcturus, its oblique ascension, oblique descension, 
and diurnal arc, at London ? 

4. Required the rising and setting amplitude of y 
Bellatrix, its oblique ascension, oblique descension, 
and diurnal arc, at London? 

Problem LXX. 

To find the distances of the stars from each other in 

degrees. 

Rule. Lay the quadrant of altitude over any two 
stars, so that the division marked o may be on one of 
the stars ; the degrees between them will show their 
distance, or the angle which these stars subtend, as 
seen by a spectator on the earth. 

Examples. 1. What is the distance between Vega in 
Lyra, and Altair in the Eagle ? 
Answer. 34 degrees. 

2. Required the distance between £ in the Bull's 
Horn, and y Bellatrix in Orion's shoulder? 



THE CELESTIAL GLOBE, 139 

3. What is the distance between in Pollux, and * 
in Procyon ? 

4. What is the distance between <, the brightest of 
the Pleiades, and a in the Great Dog's Foot? 

5. What is the distance between • in Orion's girdle, 
and ( in Cetus ? 

6. What is the distance between Arcturus in Bootes, 
and in the right shoulder of Serpentarius? 

Problem LXXI. 

To find what stars lie in or near the mootfs path, or 
what stars the moon can eclipse, or make a near ap- 
proach to. 

Rule. Find the moon's longitude and latitude, or 
her right ascension and declination, in an ephemeris, 
for several days, and mark the moon's places on the 
globe; then by laying a thread, or the quadrant of alti- 
tude, over these places, you will see nearly the moon's 
path, and consequently, what stars lie in her way. 

Examples. 1. What stars were in, or near, the 
moon's path, on the 10th, 11th, 13th, and 16th of De- 
cember, 1805? 

10th, )'s longitude a 20 ° 12 ' latitude 3° 34' S. 

11th, - - rrg 4 22 - - 4 25 S. 

13th, - - -= 1 39 - - 5 15 S. 

16th, - - m 10 11 - - 4 26 S. 

Anstoer. The stars will be found to be Cor Leonis or Regulus, Spi- 
ca Virginis, * in Libra, &c. See page 47, White's Ephemeris. 

2. On the 1st, 2d, 3d, 4th, and 5th of April, 1827, 
what stars will lie near the moon's way ? 



84 41 


- 19 59 N. 


97 14 


- 19 9N. 


109 44 


- 17 28 N. 


122 8 


- 14 58 N. 


Problem LXXII. 





140 PROBLEMS PERFORMED WITH 

1st, )'s right ascension, 72° 6' declination 19° 55'N 

2d, 

3d, 

4th, 

5th, 



Given the latitude of the place and the day of the 
month , to find what planets will be above the horizon 
after sun-setting. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place ; find 
the sun's place in the ecliptic, and bring it to the 
western part of the horizon, or to ten or twelve degrees 
below ; then look in the ephemeris for that day and 
month, and you will find what planets are above the 
horizon, such planets will be fit for observation on that 
night. 

Examples. 1. Were any of the planets visible after 
the sun had descended ten degrees below the horizon 
of London, on the 1st of December, 1805 ? Their lon- 
gitudes being as follow : 

S 8 8 22°30' 4 8 s 15° 27' )'s longitude at 

? 9 23 40 J? 6 24 50 midnight 8 9° 

$ 8 25 21 jji 6 24 5 

Answer. Venus and the moon were visible. 

2. What planets will be above the horizon of Lon- 
don when the sun has descended ten degrees below, 
on the 1st of January, 1827 ? Their longitudes being 
as follow : 



THE CELESTIAL GLOBE. 141 

$ 8 17° 51 4 6*12 9 18 ^ longitude at 

? 8 27 10 i> 3 2 1 midnight 11 s 5° 9' 

£ 11 2 48 >£ 9 23 22 * 

Problem LXXIII. 

Given the latitude of the place, day of the month, and 
hour of the night or morning, to find what planets 
will be visible at that hour. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place ; find 
the sun's place in the ecliptic, bring it to the brass me- 
ridian, and set the index of the hour-circle to 12 ; then, 
if the given time be before noon, turn the globe eastward 
till the index has passed over as many hours as the 
time wants of noon ; but if the given time be past noon, 
turn the globe westward on its axis till the index has 
passed over as many hours as the time is past noon : 
let the globe rest in this position, and look in the 
ephemeris for the longitudes of the planets, and, if any 
of them be in the signs which are above the horizon, 
such planets will be visible. 

Examples. 1. On the 1st of December, 1805, the 
longitudes of the planets, by an ephemeris, were as 
follow ; were any of them visible at London at five 
o'clock in the morning ? 

$ 8 3 22° 30' 4 8 s 15° 27' )'s longitude at 

? 9 23 40 h 6 24 50 midnight s 9° 15'. 

t 8 25 21 ij 6 24 5 

Answer. Saturn and the Georgium Sit! us were visible, and both 
nearly in the same point of the heavens, near the eastern horizon ; Sa- 
turn was a little to the north of the Georgian. 



142 PROBLEMS PERFORMED WITH 

2. On the first of June, 1827, the longitudes of the 
planets in the fourth page of the Nautical Almanac are 
as follow : will any of them be visible at London at ten 
o'clock in the evening? 

S 2 s 0° 54' 4 6 s 4° 28' )'s longitude at 

? 1 7 1 J? 3 5 47 midnight 5' 0° 25'. 

t 2 22 12 # 9 27 52 

Problem LXXIV. 

The latitude of the place and day of the month being 
given, to find how long Venus rises before the sun 
when she is a morning star, and how long she sets 
after the sun when she is an evening star. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place ; find 
the latitude and longitude of Venus in an ephemeris, 
and mark her place on the globe ; find the sun's place 
in the ecliptic, and bring it to the brass meridian ; then, 
if the place of Venus be to the right hand of the me- 
ridian, she is an evening star ; if to the left hand she is 
a morning star. 

When Venus is an evening star. Bring the sun's 
place to the western edge of the horizon, and set the 
index of the hour-circle to 12 ; turn the globe westward 
on its axis till Venus coincides with the western edge 
of the horizon ; and the hours passed over by the index 
will show how long Venus sets after the sun. 

When Venus is a morning star. Bring the sun's place 
to the eastern edge of the horizon, and set the index 
of the hour-circle to 12 ; turn the globe eastward on 
its axis till Venus comes to the eastern edge of the 



THE CELESTIAL GLOBE. 143 

horizon, and the hours passed over by the index will 
show how long Venus rises before the sun. 

Note. The same ride will serve for Jupiter, by mark- 
ing his place instead of that of Venus. 

Examples. 1. On the first of March, 1805, the 
longitude of Venus was 10 signs, 18 deg. 14 min., or 
18 deg. 14 min. in Aquarius, latitude deg. 52 min. 
south: was she a morning or an evening star? If a 
morning star, how long did she rise before the sun at 
London ; if an evening star how long did she shine after 
the sun set ? 

Answer. Venus was a morning star, and rose three quarters of an 
hour before the sun. 

2. On the 25th of October, 1805, the longitude of 
Jupiter was 8 signs 7 deg. 26 min., or 7 deg. 26 min. 
in Sagittarius, latitude deg. 29 min. north : whether 
was he a morning or an evening star ? If a morning 
star, how long did he rise before the sun at London ? 
If an evening star, how long did he shine after the sun 
set? *. 

Answer. Jupiter was an evening star, and set 1 hour and 20 min. 
after the sun. 

3. On the 1st of January, 1827, the longitude of 
Venus will be 8 signs 27 deg. 10 min., latitude 4 deg. 
29 min. north : will she be a morning or an evening 
star ? If she be a morning star, how long will she rise 
before the sun at London? If an evening star, how 
long will she shine after the sun sets ? 

4. On the seventh of July, 1827, the longitude of 
Jupiter will be 6 signs 5 deg. 46 min., latitude 1 deg. 
19 min. north ; will he be a morning or an evening 



144 PROBLEMS PER FORMED WITH 

star ? If he be a morning star, how long will he rise 
before the sun ? If an evening star, how long will he 
shine after the sun sets ? 

Problem LXXV. 

The latitude of a place and day of the month being given, 
to find the meridian altitude of any star or planet. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the given place ; 
then, 

For a star. Bring the given star to that part of the 
brass meridian, which is numbered from the equinoc- 
tial towards the poles ; the degrees on the meridian 
contained between the star and the horizon will be the 
altitude required. 

For the moon or a planet. Look in an ephemeris for 
the planet's latitude and longitude, or for its right as- 
cension and declination, for the given month and day, 
and mark its place on the globe ; bring the planet's 
place to the brass meridian ; and the number of degrees 
between that place and the horizon will be the altitude. 

Examples. 1. What is the meridian altitude of Al- 
debaran in Taurus, at London? 

Answer. 54° 36'. 

2. What is the meridian altitude of Arcturus in 
Bootes, at London ? 

3. On the first of February, 1827, the longitude of 
Jupiter will be 6 signs 14 deg. 25 min., and latitude 
1 deg. 27 min. north : what will his meridian altitude 
be at London ? 

4. On the first of November, 1827, the longitude of 



THE CELESTIAL GLOBE. 145 

Saturn will be 3 signs 20 dcg. 18 min., and latitude 
deg. 21 rain, south : what will his meridian altitude be 
at London ? 

5. On the first of April, 1827, at the time of the 
moon's passage over the meridian of Greenwich, her 
right ascension is 67° 49', and declination 19° 40' N. ; 
required her meridian altitude at Greenwich? 

6. On the 21st of December, 1827, the moon will 
pass over the meridian of Greenwich at 56 minutes 
past two o'clock in the evening ; required her meridian 
altitude ? 

The )'s right ascension at noon being 44° 49', declination 15° 51' N. 
Do. at midnight 50 58 - - - 16 58 N. 

Problem LXXVI. 

To find all those 'places on the earth to which the moon 
will be nearly vertical on any given day. 

Rule. Look in an ephemeris for the moon's lati- 
tude and longitude for the given day, and mark her 
place on the globe (as in Prob. LXV.) ; bring this 
place to that part of the brass meridian which is num- 
bered from the equinoctial towards the poles, and ob- 
serve the degree above it ; for all places on the earth 
having that latitude will have the moon vertical (or 
nearly so) when she comes to their respective meri- 
dians. 

Or : Take the moon's declination from page VI. of 
the Nautical Almanac, and mark whether it be north 
or south, then, by the terrestrial globe, or by a map, 
find all places having the same number of degrees of 
latitude as are contained in the moon's declination, 
n 2B 



146 PROBLEMS PERFORMED WITH 

and those will be the places to which the moon will be 
successively vertical on the given day. If the moon's 
declination be north, the places will be in north latitude ; 
if the moon's declination be south, they will be in south 
latitude. 

Examples. 1. On the 15th of October, 1805, the 
moon's longitude at midnight was 3 signs 29 deg. 14 
min., and her latitude 1 deg. 35 min. south ; over what 
places did she pass nearly vertical ? 

Answer. From the moon's latitude and longitude being given, her 
declination may be found by the globe to be about 19° north- The 
moon was vertical at Porto Rico, St. Domingo, the north of Jamaica, 
O'why'hee, &c. 

2. On the 9th of September, 1827, the moon's lon- 
gitude at midnight will be 1 sign 10 deg., and her 
latitude deg. 22 min. south ; over what places on the 
earth will she pass nearly vertical ? 

3. What is the greatest north declination which the 
moon can possibly have, and to what places will she be 
then vertical? 

4. What is the greatest south declination which the 
moon can possibly have, and to what places will she be 
then vertical? 

Problem LXXVII. 

Given the latitude of a place, day of the month, and the 
altitude of a star, to find the hour of the night, and the 
star's azimuth. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude : find the sun's place in the ecliptic, 



THE CELESTIAL CLOJJE. 1 17 

bring it to the brass meridian, and sot the index of the 
hour-circle to 12 ; bring the lower end of the quadrant 
of altitude to that side of the meridian oh which the 
star was situated when observed ; turn the globe west- 
ward till the centre of the star cuts the given altitude 
on the quadrant ; count the hours which the index has 
passed over, and they will show the time from noon 
when the star has the given altitude : the quadrant will 
intersect the horizon in the required azimuth. 

Examples. 1. At London, on the 28th of Decem- 
ber, the star Deneb in the Lion's tail, marked /2, was 
observed to be 40 deg. above the horizon, and east of 
the meridian : what hour was it, and what was the star's 
azimuth ? 

Answer. By bringing the sun's place to the meridian, and turning 
the globe westward on its axis till the star cuts 40 deg. of the quadrant 
east of the meridian, the index will have passed over 14 hours ; conse- 
quently, the star has 40 deg. of altitude east of the meridian, 14 hours 
from noon, or at two o'clock in the morning. Its azimuth will be 62^ 
deg. from the south towards the east. 

2. At London, on the 28th of December, the star &, 

in the Lion's tail, was observed to be westward of the 

meridian, and to have 40 deg. of altitude : what hour 

was it, and what was the star's azimuth? 

Answer. By turning the globe westward on its axis till the star cuts 
40 deg. of the quadrant west of the meridian, the index will have passed 
over 20 hours ; consequently, the star has 40 deg. of altitude west of 
the meridian, 20 hours from noon, or at eight o'clock Li the morning. 
Its azimuth will be 62£ deg. from the south towards the west. 

3. At London, on the 1st of September, the altitude 
of Benetnach in Ursa Major, marked ■<, was observed 
to be 36 degrees above the horizon, and west of the 
meridian ; what hour was it, and what was the star's 
azimuth? 



148 PROBLEMS PERFORMED WITH 

4. On the 21st of December, the altitude of Sirius, 
when west of the meridian at London, was observed to 
be 8 deg. above the horizon ; what hour was it, and 
w r hat was the star's azimuth? 

5. On the 12th of August, Menkar in the Whale's 
jaw, marked «, was observed to be 37 deg. above the 
horizon of London, and eastward of the meridian ; 
what hour was it, and what was the star's azimuth ? 

Problem LXXVIII. 

Given the latitude of a place, day of the month, and hour 
of the day, to find the altitude of any star, and its 
azimuth. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude ; find the sun's place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour-circle to 12 ; then, if the given time be before 
noon ; turn the globe eastward on its axis till the in- 
dex has passed over as many hours as the time wants 
of noon ; if the time be past noon, turn the globe west- 
ward till the index has passed over as many hours as 
the time is past noon : let the globe rest in this posi- 
tion, and move the quadrant of altitude till its gradua- 
ted edge coincides with the centre of the given star ; 
the degrees on the quadrant, from the horizon to the 
star, will be the altitude ; and the distance from the 
north or south point of the horizon to the quadrant, 
counted on the horizon, will be the azimuth from the 
north or south. 



THE CELESTIAL GLOBE. 149 

Examines. 1. What arc the altitude and azimuth 
of Gapella at Rome, when it is five o'clock in the morn- 
ing on the 2d of December? 

Answer. The altitude is 41 deg. 58 min. and the azimuth 60 deg. 
50 min. from the north towards the west 

2. Required the altitude and azimuth of Altair in 
Aquila on the 6th of October, at nine o'clock in the 
evening, at London ? 

3. On what point of the compass does the star Aide- 
baran bear at the Cape of Good Hope, on the 5th of 
March, at a quarter past eight o'clock in the evening; 
and what is its altitude ? 

4. Required the altitude and azimuth of Acyone in 
the Pleiades marked *, on the 21st of December, at four 
o'clock in the morning, at London ? 

Problem LXXIX. 

Given the latitude of the place, day of the month, and 
azimuth of a star, to find the hour of the night and 
the star's altitude. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude ; find the sun's place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour-circle to twelve ; bring the lower end of the qua- 
drant of altitude to coincide with the given azimuth on 
the horizon, and hold it in that position ; turn the globe 
westward till the given star comes to the graduated 
edge of the quadrant, and the hours passed over by the 
index will be the time from noon ; the degrees on the 
w2 2 b 2 



150 TROBLEMS PERFORMED WITH 

quadrant, reckoning from the horizon to the star, will 
be the altitude. 

Examples. 1. At London, on the 28th of Decem- 
ber, the azimuth of Deneb in the Lion's tail marked & 9 
was 62i deg. from the south towards the west; what 
hour was it, and what was the star's altitude ? 

Answer. By turning the globe westward on its axis, the index will 
pass over 20 hours before the star intersects the quadrant ; therefore 
the time will be 20 hours from noon, or eight o'clock in the morning ; 
and the star's altitude will be 40 deg. 

2. At London, on the 5th of May, the azimuth of 
Cor Leonis, or Regulus, marked *, was 74 deg. from 
the south towards the west ; required the star's altitude, 
and the hour of the night ? 

3. On the 8th of October, the azimuth of the star 
marked £, in the shoulder of Auriga, was 50 deg. from 
the north towards the east; required its altitude at Lon- 
don, and the hour of the night ? 

4. On the 10th of September, the azimuth of the 
star marked *, in the Dolphin, was 20 deg. from the 
south towards the east ; required its altitude at London, 
and the hour of the night ? 

Problem LXXX. 

Two stars being given, the one on the meridian, and the 
other on the east or west part of the horizon, to find 
the latitude of the place. 

Rule. Bring the star which was observed to be on 
the meridian, to the brass meridian ; keep the globe 
from turning on its axis, and elevate or depress the 
pale till the other star comes to the eastern or western 



THE CELESTIAL GLOBE. 151 

part of the horizon ; then the degrees from the ele- 
vated pole to the horizon will be the latitude. 

Examples. 1. When the two pointers of the Great 
Bear, marked * and £, or Dubhe and £, were on the 
meridian, I observed Vega in Lyra to be rising; re- 
quired the latitude? 
Answer. 27 deg. north. 

2. When Arcturus in Bootes was on the meridian, 
Altair in the Eagle was rising ; required the latitude ? 

3. When the star marked in Gemini was on the 
meridian, 1 in the shoulder of Andromeda was setting; 
required the latitude? 

4. In what latitude are » and 0, or Sirius and £ in 
Canis Major rising, when Algenib, or *, in Perseus, is 
on the meridian ? 

Problem LXXXL 

The latitude of the place, the day of the month, and 
two stars that have the same azimuth, being given, to 
find the hour of the night. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude ; find the sun's place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour-circle to 12 ; turn the globe on its axis from east 
to west till the two given stars coincide with the gra- 
duated edge of the quadrant of altitude ; the hours 
passed over by the index will show the time from noon ; 
and the common azimuth of the two stars will be found 
on the horizon. 



152 PROBLEMS PERFORMED WITH 

Examples. 1. At what hour at London, on the 1st 
of May, will Altair in the Eagle; and Vega in the Harp, 
have the same azimuth, and what will that azimuth be? 

Answer. By bringing the sun's place to the meridian, &c. and turn- 
ing the globe westward, the index will pass over 15 hours before the 
stars coincide with the quadrant ; hence they will have the same azi- 
muth at 15 hours from noon, or at three o'clock in the morning ; and 
the azimuth will be 42| deg. from the south towards the east. 

2. On the 10th of September, what is the hour at 
London, when Deneb in Cygnus, and Markab in Pe- 
gasus, have the same azimuth, and what is the azimuth ? 

3. At what hour on the 15th of April will Arcturus 
and Spica Virginis have the same azimuth at London, 
and what will that azimuth be ? ♦ 

4. On the 20th of February, what is the hour at 
Edinburgh when Capella and the Pleiades have the 
same azimuth, and what is the azimuth ? 

5. On the 21st of December, what is the hour at 
Dublin when * or Algenib in Perseus, and £ in the 
Bull's horn, have the same azimuth, and what is the 
azimuth ? 

Problem LXXXII. 

The latitude of the place, the day of the month, and two 
stars that have the same altitude, being given, to find 
the hour of the night. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude ; find the sun's place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour-circle to 12 ; turn the globe on its axis from east 



L 



THE CELESTIAL GLOBE. 153 

to west till the two given stars coincide with the given 
altitude on the graduated edge of the quadrant ; the 
hours passed over by the index will be the time from 
noon when the two stars have that altitude. 

Examples. 1. At what hour at London, on the 2d 
of September, will Markab in Pegasus, and « in the 
head of Andromeda, have each 30 deg. of altitude ? 

Answer. At a quarter past eight in the evening. 

2. At what hour at London, on the 5th of January, 
will », Menkar, in the Whale's jaw, and «, Aldebaran, 
in Taurus, have each 35 deg. of altitude ? 

3. At what hour at Edinburgh, on the 10th of No- 
vember, will «, Altair, in the body of the Eagle, and r, 
in the tail of the Eagle, have each 35 deg. of altitude? 

4. At what hour at Dublin, on the 15th of May, 
will ■<, Benetnach, in the Great Bear's tail, andr, in the 
shoulder of Bootes, have 56 deg. of altitude? 

Problem LXXXIII. 

The altitudes of two stars having the same azimuth, 
and that azimuth being given, to find the latitude of 
the place. 

Rule. Place the graduated edge of the quadrant of 
altitude over the two stars, so that each star may be 
exactly under its given altitude on the quadrant ; hold 
the quadrant in this position, and elevate or depress the 
pole till the division marked o, on the lower end of the 
quadrant, coincides with the given azimuth on the ho- 
rizon : when this is effected, the elevation of the pole 
will be the latitude. 



154 PROBLEMS PERFORMED WITH 

Examples. 1. The altitude of Areturus was ob- 
served to be 40 deg. and that of Cor. Caroli 68 deg. ; 
their common azimuth at the same time was 71 deg. 
from the south towards the east ; required the latitude ? 

Answer. 5H deg. north. 

2. The altitude of * in Castor was observed to be 40 
deg., and that of p in Procyon 20 deg. ; their common 
azimuth at the same time was 73J deg. from the south 
towards the east ; required the latitude ? 

3. The altitude of «, Dubhe, was observed to be 40 
deg., and that of r in the back of the Great Bear 29 \ 
deg., their common azimuth at the same time was 30 
deg. from the north towards the east ; required the la- 
titude ? 

4. The altitude of Vega, or « in Lyra, was observed 
to be 70 deg., and that of * in the head of Hercules 
39^ deg., their common azimuth at the same time was 
60 deg. from the south towards the west ; required the 
latitude ? 

Problem LXXXIV. 

The day of the month being given, and the hour when 
any known star rises or sets, to find the latitude of 
the place. 

Rule. Find the sun's place in the ecliptic, bring 
it to the brass meridian, and set the index of the hour- 
circle to 12 ; then, if the given time be. before noon, 
turn the globe eastward till the index has passed over 
as many hours as the time wants of noon ; but, if the 
given time be past noon, turn the globe westward till 
the index has passed over as many Jiours as the time 



THE CELESTIAL GLOBE. 155 

ifl past noon; elevate or depress the pole till the cen- 
tre of the given star coincides with the horizon; then 
(lie elevation of the pole will show the latitude. 

Examples. 1. In what latitude does .<, Mirach, in 
Bootes, rise at half past twelve o'clock at night, on the 
tenth of December ? 

Answer. 51£ deg. north. 

2. In what latitude does Cor I^eonis, or Regulus, 
rise at ten o'clock at night, on the 21st of January? 

3. In what latitude does 3, Rigel in Orion, set at 
four o'clock in the morning, on the 21st of December? 

4. In what latitude does £, Capricornus, set at eleven 
o'clock at night, on the 10th of October? 

Problem LXXXV. 

To find on what day of the year any given star passes 
the meridian at any given hour. 

Rule. Bring the given star to the brass meridian, 
and set the index to 12 ; then, if the given time be 
before noon, turn the globe westward till the index has 
passed over as many hours as the time wants of noon ; 
but, if the given time be past noon, turn the globe 
eastward till the index has passed over as many hours 
as the time is past noon ; observe that degree of the 
ecliptic which is intersected by the graduated edge of 
the brass meridian, and the day of the month answering 
thereto, on the horizon, will be the day required. 

Examples. 1 . On what day of the month does Pro- 
cyon come to the meridian of London at three o'clock 
in the morning? 
Answer. Here the time is nine hours before noon,- the globe must 



156 PKOELEHIS l'EIiFOKMED WITH 

therefore be turned nine hours towards the west, the point of the eclip 
tic intersected by the brass meridian will then be the ninth of f, an 
swering nearly to the first of December. 

2. On what day of the month, and in what month 
does *, Alderamin, in Cepheus, come to the meridian of 
Edinburgh at ten o'clock at night? 

Answer. Here the time is ten hours after noon ; the globe must 
therefore be turned ten hours towards the east, the point of the ecliptic 
intersected by the brass meridian will then be the 17th of irg, answering 
to the ninth of September. 

3. On what day of the month, and in what month, 
does £| Deneb, in the Lion's tail, come to the meri- 
dian of Dublin at nine o'clock at night ? 

4. On what day of the month, and in what month, 
does Arcturus in Bootes come to the meridian of Lon- 
don at noon ? 

5. On what day of the month, and in what month, 
doeskin the Great Bear come to the meridian of Lon- 
don at midnight? 

6. On what day of the month, and in what month, 
does Aldebaran come to the meridian of Philadelphia 
at five o'clock in the morning at London ? 

Problem LXXXVI. 

The day of the month being given, to find at what hour 
any given star comes to the meridian. 

Rule. Find the sun's place in the ecliptic, bring 
it to the brass meridian, and set the index of the hour- 
circle to 12 ; turn the globe westward on its axis till 
the given star comes to the brass meridian, and the 
hours passed over by the index will be the time from 
noon when the star culminates. 



the celestial globe. 157 

Or, without the globe. 

Subtract the right ascension of the sun for the given 
lay from the right ascension of the star, and the remain- 
ier will be the time of the star's culminating nearly. 
f the sun's right ascension exceeds the star's add 24 
lours to the star's before you subtract. 

Examples. 1. At what hour does Cor Leonis, or 
Etegulus, come to the meridian of London on the 23d 
)f September ? 

Answer. The index will pass over 21 £ hours ; hence this star cul- 
lunates or comes to the meridian 21$ hours after noon, or at three 
quarters past nine o'clock in the morning. 

2. At what hour does Arcturus come to the meri- 
dian of London on the 9th of February ? 

Answer. The index will pass over 16£ hours ; hence Arcturus cul- 
minates 16£ hours after noon, or at half past four o'clock in the morn- 
ing. 

3. Required the hours at which the following stars 

come to the meridian of London on the respective days 
annexed : 



Bellatrix, January 9th, 
Menkar, May 18th. 

* Draco, Sept. 22d. 

* Dubhe, Dec. 20th. 



& Mirach, October 5th. 
Aldebaran, Feb. 12th. 
(8 Aries, November 5th. 
\ Taurus, January 24th. 



4. At what time will Sirius come to the meridian of 
Greenwich on the 18th of December, 1827, his right 
ascension being 99° 15' 26", and the sun's right as- 
cension 265° 29' 0". 

o 2C 



158 PROBLEMS PERFORMED WITH 



Problem LXXXVII. 

Given the azimuth of a known star, the latitude, and the 
hour, to find the star's altitude and the day of the 
month. 

Rule. Bring the pole so many degrees above the 
horizon as are equal to the latitude of the given place, 
screw the quadrant of altitude upon the brass meridiau 
over that latitude, bring the division marked o on the 
lower end of the quadrant to the given azimuth on the 
horizon, turn the globe till the star coincides with the 
graduated edge of the quadrant, and set the index of 
the hour-circle to 12 ; then if the given time be before 
noon, turn the globe westward till the index has passed 
over as many hours as the time wants of noon ; if the 
given time be past noon, turn the globe eastward till 
the index has passed over as many hours as the time is 
past noon ; observe that degree of the ecliptic which 
is intersected by the graduated edge of the brass meri- 
dian, and the day of the month answering thereto, on 
the horizon, will be the day required. 

Examples. 1. At London, at ten o'clock at night, 
the azimuth of Spica Virginis was observed to be 40 
deg. from the south towards the west ; required its alti- 
tude, and the day of the month ? 

Answer. The star's altitude is 20 deg. and the day is the 18th of 
June. The time being ten hours past noon, the globe must be turned 
ten hours towards the east. 

2. At London, at four o'clock in the morning, the 



THE CELESTIAL GLOBE. 159 

azimuth of Arcturus was 70 cleg, from the south to- 
wards the west ; required its altitude, and the day of 
the month ? 

Answer. Here the time wants eight hours of noon, therefore the 
globe must be turned eight hours westward ; the altitude of the star 
will be found to be 40 deg., and the day the 12th of April. 

3. At Edinburgh, at 11 o'clock at night, the azimuth 
of « Serpentarius, or Ras Alhagus, was 60 deg. from 
the south towards the east ; required its altitude, and 
the day of the month ? 

4. At Dublin at two o'clock in the morning, the 
azimuth of Pegasus, or Scheat, was 70 deg. from 
the north towards the east ; required its altitude, and 
the day of the month ? 

Problem LXXXVIII. 

The altitudes of tivo stars being given, to find the lati* 
tude of the place. 

Rule. Subtract each star's altitude from 90 de- 
grees ; take successively the extent of the number of 
degrees, contained in each of the remainders, from the 
equinoctial, with a pair of compasses ; with the com- 
passes thus extended, place one foot successively in the 
centre of each star, and describe arcs on the globe with 
a black-lead pencil ; these arcs will cross each other in 
the zenith ; bring the point of intersection to that part 
of the brass meridian which is numbered from the 
equinoctial towards the poles, and the degree above it 
will be the latitude. 

Examples. 1. At sea, in north latitude, I observed 



160 PEOBLEMS PERFORMED WITH 

the altitude of Capella to be 30 deg., and that of Alde- 
baran 35 deg. ; what latitude was I in ? 

Answer. With an extent of 60 deg. (=90°-— 30°) taken from the 
equinoctial, and one foot of the compasses in the centre of Capella, de- 
scribe an arc towards the north ; then with 55 deg. (, = 90° — 35°,) taken 
in a similar manner, and one foot of the compasses in the centre of Al- 
debaran, describe another arc, crossing the former ; the point of inter- 
section brought to the brass meridian will show the latitude to be 20£ 
deg. north. 

2. The altitude of Markab in Pegasus was 30 deg., 
and that of Altair in the Eagle, at the same time, was 
65 deg. ; what was the latitude, supposing it to be 
north ? 

3. In north latitude the altitude of Arcturus was ob- 
served to be 60 deg., and that of /3 or Deneb, in the 
Lion's tail, at the same time, was 70 deg. ; what was 
the latitude ? 

4. In north latitude, the altitude of Procyon was 
observed to be 50 deg. and that of Betelgeux in Orion, 
at the same time, was 58 deg. ; required the latitude 
of the place of observation ? 

Problem LXXXIX. 

The meridian altitude of a known star being given at 
anyplace in north latitude, to find the latitude. 

Rule. Bring the given star to that part of the brass 
meridian which is numbered from the equinoctial to- 
wards the poles ; count the number of degrees in the 
given altitude on the brass meridian from the star to- 
wards the south part of the horizon, and mark where 
the reckoning ends ; elevate or depress the pole till this 
mark coincides with the south point of the horizon, 



THE CELESTIAL GLOBE. 161 

and the elevation of the north pole above the north 
point of the horizon will show the latitude. 

Examples. 1. In what degree of north latitude is 
the meridian altitude of Aldebaran 52^ deg. ? 
Answer. 53 deg. 36 min. north. 

2. In what degree of north latitude is the meridian 
altitude of 0, one of the pointers in Ursa Major, 90 deg. ? 

3. In what degree of north latitude is y, in the head 
of Draco, vertical when it culminates ? 

4. In what degree of north latitude is the meridian 
altitude of * or Mirach in Bootes, 68 deg. ? 

Problem XC. 

TJie latitude of a place, day of the month, and hour of 
thd day, being given, to find the nonagesimal de- 
gree* of the ecliptic, its altitude and azimuth, and 
the medium cgeli. 

Rule. Elevate the north pole to the latitude of the 
given place, and screw the quadrant of altitude upon 
the brass meridian over that latitude ; find the sun's 
place in the ecliptic, bring it to the brass meridian, 
and set the index of the hour-circle to 12 ; then, if the 
given time be before noon, turn the globe eastward till 
the index has passed over as many hours as the time 
wants of noon ; but, if the given time be past noon, 

* The nonagesimal degree of the ecliptic is 'that point which is the 
most elevated above the horizon, and is measured by the angle which 
the ecliptic makes with the horizon at any elevation of the pole ; or, it is 
the distance beneath the zenith of the place and the pole of the eclip- 
tic. This angle is frequently used in the calculation of solar eclipses. 
The medium coeli, or mid-heaven, is that point of the ecliptic which is 
upon the meridian. 

o 2 2 c 2 



162 PROBLEMS PERFORMED WITH 

turn the globe westward till the index has past over 
as many hours as the time is past noon, and fix the 
globe in this position ; count 90 deg. upon the ecliptic 
from the horizon, (either eastward or westward) and 
mark where the reckoning ends, for that point of the 
ecliptic will be the nonagesimal degree, and the degree 
of the ecliptic cut by the brass meridian will be the 
medium cceli : bring the graduated edge of the qua- 
drant of altitude to coincide with the nonagesimal de- 
gree of the ecliptic thus found, and the number of de- 
grees on the quadrant, counted from the horizon, will 
be the altitude of the nonagesimal degree ; the azimuth 
will be seen on the horizon. 

Examples. 1. On the 21st of June, at forty-five 
minutes past three o'clock in the afternoon at London, 
required the point of the ecliptic which is the nonage- 
simal degree, its altitude and azimuth, the longitude 
of the medium cceli, and its altitude, &c. 

Answer. The nonagesimal degree is 10 deg. in Leo, its altitude is 
54 deg., and its azimuth 22 deg. from the south towards the west, or 
nearly S. S. W. The mid-heaven, or point of the ecliptic under the 
brass meridian, is 24 deg. in Leo, and its altitude above the horizon, is 
52 deg. The degree of the equinoctial cut by the brass meridian reck- 
oning from the point Aries, is the right ascension of the mid-heaven, 
which in this example is 146 deg. The rising point of the ecliptic will 
be found to be 10 deg. in Scorpio, and the setting point 10 deg. in Tau- 
rus. If the graduated edge of the quadrant be brought to coincide with 
the sun's place, the sun's altitude will be found to be 39 deg. and his 
azimuth 78£ deg. from the south towards the west, or nearly W. by S. 

2. At London, on the 24th of April, at nine o'clock 
in the morning ; required the point of the ecliptic which 
is the nonagesimal degree, its altitude and azimuth, the 
point of the ecliptic which is the raid-heaven, &c. &c. ? 



THE CELESTIAL GLOBE. 163 

3. At Limerick, in 52 deg. 22 min. north latitude, 
on the 15th of October, at five o'clock in the afternoon ; 
required the point of the ecliptic which is the nonage- 
simal degree, its altitude and azimuth, the point of the 
ecliptic which is the mid-heaven, &c. &c. ? 

4. At Dublin, in latitude 53 deg. 21 min. north, on 
the 15th of January, at two o'clock in the afternoon ; 
required the longitude, altitude, and azimuth, of the 
nonagesimal degree ; and the longitude and altitude of 
the mediun cceli, &c. &c. ? 

Problem XCI. 

The latitude of a place, day of the month, and the hour, 
together with the altitude and azimuth of a star, being 
given, to find the star. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place;, and 
screw the quadrant of altitude on the brass meridian 
over that latitude ; find the sun's place in the ecliptic, 
bring it to the brass meridian, and set the index of 
the hour-circle to 12 ; then, if the given time be before 
noon, turn the globe eastward till the index has passed 
over as many hours as the time wants of noon , but, if 
the time be past noon, turn the globe westward till the 
index has passed over as many hours as the time is past 
noon ; let the globe rest in this position, and bring the 
division marked O on the quadrant to the given azi- 
muth on the horizon ; then, immediately under the 
given altitude on the graduated edge of the quadrant, 
you will find the star. 

Examples. 1. At London, on the 21st of Decern- 



164 PROBLEMS PERFORMED WITH 

ber, at four o'clock in the morning, the altitude of a 
star was 50 deg., and its azimuth was 37 deg. from the 
south towards the east ; required the name of the star ? 

Answer. Deneb, or ,3 in the Lion's tail. 

2. The altitude of a star was 27 deg., its azimuth 
76J deg. from the south towards the west, at eleven 
o'clock in the evening at London, on the 11th of May ; 
what star was it ? 

3. At London, on the 21st of December, at four 
o'clock in the morning, the altitude of a star was 8 deg., 
and its azimuth 51 deg. from the south towards the 
west ; required the name of the star ? 

4. At London, on the 1st of September, at nine 
o'clock in the evening, the altitude of a star was 47 
deg., and its azimuth 73 deg. from the south towards 
the east ; required the name of the star ? 



p 



ROBLEM XC.IL 



To find the time of the moon's southing, or coming to 
the meridian of any place, on any given day of the 
month. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the given place ; 
find the moon's latitude and longitude, or her right as- 
cension and declination, from an ephemeris, and mark 
her place on the globe ; bring the sun's place to the 
brass meridian, and set the index of the hour-circle to 
12 ; turn the globe westward till the moon's place 
comes to the meridian, and the hours passed over by 
the index will show the time from noon when the moon 
will be upon the meridian. 



the celestial globe. 165 

Or, without the globe. 

Find the moon's age, which multiply by 81, and cut 
off two figures from the right hand of the product, the 
left hand figures will be the hours; the right hand 
figures must be multiplied by 60, for minutes. 

Or, correctly, thus : 

Take the difference between the sun's and moon's 
right ascension in 24 hours ,* then, as 24 hours dimi- 
nished by this difference is to 24 hours, so is the moon's 
right ascension at noon, diminished by the sun's, to the 
time of the moon's transit. 

Examples. 1. At what hour, on the 10th of April, 
1827, will the moon pass over the meridian of Green- 
wich ? The moon's right ascension at midnight being 
185 deg. 28 min., and her declination 5 deg. 49 min. 
south. 

Ansuwr. By tfie Globe.— -The moon comes to the meridian about 
midnight. 

By using the Nautical Almanac. 

Sun's right ascension at noon 10th April = 1 h. 13 7 15" 7 
Ditto .... llthApril = l 16 55 5 



Increase of motion in 24 hours . 3 39 8 



Moon's right ascension at noon 10th April = 178° 47' 32" 
Ditto . 11th April = 192° 16' 45" 



Increase in 24 hours .... 13° 29' 13" equal 



to 53' 56"; hence 59' 56" diminished by 3' 39", leaves 5(V 17" the moon's 
motion exceeds the sun's in 24 hours. 



166 PROBLEMS PERFORMED WITH 

Moon's right ascension 178° 47' x 4 = * 11 h. 55' 8" 
Sun's right ascension = 1 13 15.7 



10 41 52.3 
24h — 5C 17" : 24h. : : 10° 41' : llh. 4' the true time of the moon's pas- 
sage over the meridian in the morning, agreeing within one minute of 
the Nautical Almanac. 

2. At what hour, on the 1st of January, 1827, will 
the moon pass over the meridian of Greenwich, the 
moon's right ascension at noon being 328 deg. 43 min., 
and declination 7 deg. 15 min. south. 

3. At what hour, on the 12th of March, 1827, will 
the moon pass over the meridian at Greenwich, the 
moon's right ascension at midnight being 164 deg. 41 
min., and declination 1 deg. 43 min. north? 

4. At what hour, on the 17th of October, 1827, will 
the moon pass over the meridian of Greenwich, the 
moon's right ascension at noon being 163 deg. 28 min., 
and declination 2 deg. 33 min. north ? 

Problem XCIII. 

The day of the month, latitude of the place, and time 
of high water at the full and change of the moon be- 
ing given, to find the time of high ivater on the given 
day. 

Rule. Find the time at which the moon comes to 
the meridian of the given place by the preceding pro- 
blem, to which add the time of high water at the given 
place at the full and change of the moon, and the sum 
will show the time of high water in the afternoon. If 

* When the sun's right ascension is greater than the moon's, 24 hours 
must be added to the moon's right ascension before you subtract. 



THE CELESTIAL GLOBE. 1G7 

the sum exceed 12 hours, subtract 12 hours and 24 

minutes from it, and the remainder will show the time 

of high water in the morning ; but if the sum exceed 

24 hours, subtract 24 hours and 48 minutes from it, 

and the remainder will show the time of high water in 

the afternoon. 

Examples. 1. Required the time of high water at 

London Bridge on the 2d of April, 1827, the moon's 

right ascension at that time being 78 deg. 23min.,and 

her declination 20 deg. 4 min. north ? 

Answer, By the Globe. — The moon comes to the meridian at 4h 39' 
Time of high water at the full and change at London - 3 



Time of high water in the morning .... 7 39 



2. Required the time of high water at Hull, on the 
25th of May, 1827, the moon's right ascension at noon 
being 58 deg. 34 min., and her declination 18 deg. 50 
min. north ? 

3. Required the time of high water at Liverpool, on 
the 22d of June, 1827, the moon's right ascension at 
noon being 68 deg. 2 min., and her declination 19 deg. 
39 min. north ? 

4. Required the time of high water at Limerick, on 
the 19th of August, 1827, the moon's right ascension 
at noon being 111 deg. 20 min., and her declination 17 
deg. 10 min. north? 

5. Required the time of high water at Bristol, on 
the 9th of September, 1827, the moon's right ascension 
at noon being 31 deg. 51 min., and her declination 13 
deg. 6 min. north ? 

6. Required the time of high water at Dublin, on 



168 PROBLEMS PERFORMED WITH 

the 12th of October, 1827, the moon's right ascension 
at noon being 102 degrees 57 min., and her declination 
18 deg. 3 min. north? 

Problem XC1V. 

To describe the apparent path of any planet, or of a 
comet, amongst the fixed stars, fyc. 

Rule. Draw a straight line o, o, to represent the 
ecliptic, and divide it into any convenient number of 
equal parts. Set off eight of those equal parts north- 
ward and southward of the ecliptic at each end thereof; 
and draw lines, as in the figure Plate V.; these will re- 
present the zodiac. Find the planet's geocentric lati- 
tude and longitude in an ephemeris, or in the Nautical 
Almanac, and mark its place for every month, or for 
several days in each month, beginning at the right 
hand of the ecliptic line, and proceeding towards the 
left.* 

Find the latitudes and longitudes f of the principal 
stars in the several constellations near which the planet 
passes, and set them off in a similar manner from the 
right hand towards the left ; you will thus have a com- 
plete picture of any part of the heavens, with the posi- 

* The young student will recollect, that the stars appear in a con- 
trary order in the heavens to what they do on the surface of a globe. 
In the heavens we see the concave part, on the globe the convex. 
This manner of delineating the stars Will be found extremely useful, 
and will enable the student to know their names and places sooner than 
by the globe. 

I The places of the stars may likewise be laid down by their right 
ascensions and declinations, by drawing a portion of the equinoctial 
instead of the ecliptic. 



Till: CELESTIAL GLOUE. 



109 



tions of the several stars, &c. as they appear to a spec- 
tator on the earth. 

ExAMrLE. Delineate the path of the planet Jupiter 
for the year 1811 ; the latitudes and longitudes being 
as fellow :* 



Longitudes. Latitudes. 

Jan. 1st. l s 21°45' n 57'S. 
Feb. 7th 12211 
25th 123 58 



March 1st 1 24 29 
25th 128 16 

April 1st 129 35 

25th 2 4 30 

May 1st 2 5 49 

13th 2 8 31 

25th 2 11 17 

June 1st 2 12 54 

25th 2 18 27 

July 7th 2 21 49 



47S. 
43S. 
42S. 

37S. 
36S. 
32 S. 
31S. 
30 S. 
29S. 
28 S. 
26S. 
25S. 



Longitudes. Latitudes. 

July 25th 2 S 25°1' 0°24'S. 
Aug. 7th 2 27 36 

19th 2 29 48 

25th 3 48 



Sept. 7th 3 

25th 3 

Oct. 7th 3 
-25th 3 
1st 3 
19th 3 
25th 3 
13th 3 
25th 3 



Nov. 



Dec, 



2 45 

4 50 

5 44 

6 15 
6 10 
5 12 
4 40 
2 34 
57 



23 S. 
22 S. 
22 S. 
21 S. 
21 S. 
20 S. 
19 S. 
18 S. 
17 S. 
16 S. 
14 S. 
12 S. 



Jupiter's path, when delineated, will be south of the 
ecliptic in the order A, B, C, D, E, F, G, H. Thus, 
he will appear at A on the 1st of January, at B on the 
1st of March, at C on the 1st of April, at D on the 1st 
of May, at E on the 1st of June, at F on the 7th of 
July, at G on the 25th of August, and at H on the 25th 
of October. On the 25th of August, when Jupiter ap- 
pears at G, he will be a little to the right hand of the 
star marked i in Gemini ; when he arrives at H, which 
will happen on the 25th of October, he will apparently 
return again to G, a small matter above his former path, 

*As Jupiter performs his revolution round the sun in 11 years 315 
days, he will have nearly the same longitude in the years 1823 and 1835, 
consequently he will pass through the same constellations as are deli- 
neated in Plate V. 

V 2D 



170 PROBLEMS PERFORMED, &C. 

where he will be situated on the 25th of December. 
Jupiter will not be visible during the whole of his ap- 
parent progress from A to H, being too near to the sun 
during the months of May and June. 

In the same manner the places and situations of the 
stars may be delineated ; thus, Aldebaran, the princi- 
pal star in the Hyades, will be found by the globe, (or 
a proper table) to be situated in 7° of n and in 5|° of 
south latitude ; Betelgeux in Orion's right shoulder, 
in about 26° of n and 16° of south latitude, and its 
place may be laid down on a map by extending the line 
of its longitude, as frornL, till it meets a straight line 
passing through 16, 16, on the sides of the map. In 
the same manner any other star's situation may be de- 
scribed ; thus the Hyades will appear at Q, the Pleia- 
des at P, &c. and Bellatrix, &c. as in the figure. 

The constellation Orion, here described, is a very 
conspicuous object in the heavens in the months of 
January and February, about 9 or 10 o'clock in the 
evening, and will be an excellent guide for determining 
the positions of several other constellations, particularly 
Canis Major, Canis Minor, Auriga, &c. 



QUESTIONS 

FOR EXAMINATION OF PUPILS. 



CHAPTER I. 

What is the terrestrial globe ?— the celestial ? 

What is the axis of the earth ? 

How is it represented ? 

What are the poles of the earth ?— the celestial poles ? 

What is the brazen meridian ? 

How is it divided? — marked ? 

What are great circles ?— small circles? — meridians? When is it 
noon ? What is the first meridian ? — the equator? 

How are the latitudes of places reckoned ? — the longitudes ? 

What is the equinoctial ? 

How are declinations and right ascensions reckoned ? 

What is the ecliptic ? — the zodiac ? How are the ecliptic and zodiac 
divided ? Name the spring signs — summer — autumnal — winter. 

Which are the ascending signs ? — the descending signs ? 

What are the colures ? 

How do they divide the ecliptic ? 

What is meant by declination ? 

When has the sun no declination? 

When is his declination north ? — when south? — when greatest? 

What is the greatest declination of a star ? — a planet ? 

What are the tropics ? Of what are they the limits? 

What are the polar circles ? 

What are parallels oflatitr.de ? 

Is their number limited ? 

What is the hour-circle on the artificial globe? How is it divided ? 
What is its use ? 

What is the horizon ? — the sensible horizon ? -the rational horizon ? — 
the wooden horizon of the artificial globe ? 

What is marked on its first circle ? — the second — third — fourth — fiflh 
—sixth — seventh — eighth ? 

171 



172 QUESTIONS FOR EXAMINATION. 

What are the cardinal points of the horizon ? — of the heavens ? — of 
the ecliptic ? 

What is the zenith ? — the nadir ? 

What is the pole of any circle ? Give examples. 

What are the equinoctial points ? — the solstitial ? 

What happens when the sun is one of the equinoctial points? — the 
solstitial ? 

What is an hemisphere ? 

What hemisphere does the horizon divide ? — the equator ? — the brass 
meridian ? 

What is the Mariner's compass ? 

Describe it. 

What is the variation of the compass ? 

When is the variation east ? — when west ? 

What is the variation in England ? 

What is the latitude of a place ? — how reckoned ? — The latitude of 
a star or planet ? — how reckoned ? What is the greatest possible lati- 
tude of a star ? — a planet ? — of the sun ? 

What is the quadrant of altitude ? 

What is the use of the upper division ? — the lower ? 

What is the longitude of a place ? — how reckoned ? What is the 
greatest possible longitude of a place ? 

What is the longitude of a star or planet ? — of the sun ? 

What are almacanters ? 

Are they drawn on the globe ? How are they described ? 

What are parallels of celestial latitude? — parallels of declination ? — 
Azimuth or vertical circles ? 

What are measured on them ? 

How are they represented ? 

What is the prime vertical ? 

What is the altitude of any object in the heavens ? 

When is it called meridian altitude ? 

What is the zenith distance of a celestial object ? — when is it called 
meridian zenith distance ? 

What is the polar distance of any celestial object? 

What is the amplitude of an object in the heavens ? For what is it 
used ? When has the sun north amplitude ? — when south ? When has 
it none? 

What is the azimuth of a celestial object? 

What are hour-circles ? 



QUESTIONS FOR EXAMINATION. 173 

What is meant by a right sphere ? — a parallel sphere ?— an oblique 
sphere I 

What is meant by climate ? 

What is a zone ? How many are there ? How many climates are 
there ? What is the torrid zone ? What opinion was entertained by 
the ancients ? What are the temperate zones — the frigid zones ? What 
is meant by amphiscii ? — ascii ? — heteroscii ? — periscii ? — antceci ? — pe- 
rioeci ? — antipodes ? — right ascension ? — oblique ascension ? — oblique 
descension?— ascensional or descensional difference? — crepusculum? 
— the angle of position? 

What method of describing the stars is now used ? Who invented 
it ? How has it been further enlarged ? How are double stars desig- 
nated ? — how discovered ? 

Repeat the Greek alphabet ? 

What is meant by the diurnal arc ?— the noctural arc ?— aberration ? 



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